I can't help much since I don't paint, but I'm pretty sure you having SAI has nothing to do with anything since you can create and import custom brushes.

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laaaaaaaaaaaaaaaaaaaaaayeeeeeeeeeeers

your backgrounds are really nice, but currently they look like 3D CAD drawings without the final finish. so your things arent overly flat in their contour, but the lack of shadows and lightness of those that exist, the stark midday lighting, takes away from the mood.
the great thing about the concept art youre drawing inspiration from, in part, is its concentrated and directional lighting. the light areas are light, the dark areas are very dark. also, theres an overall colour tint that comes with light - photographers prefer to shoot in the early morning and late evening, the "golden hour" because the colour temperature of the light is lower, more golden, and gives things greater richness.
In that last image you shared, the palette is overwhelmingly green with a little blue, not exactly because the light is, but because of reflections from the grass and the sky, and it gives a greater sense of place (and time and temperature) as well as making an altogether more appealing image

so, consider the direction of and nature of your light - the longer the shadows and more concentrated the point of light (hence greater contrast) the more dramatic it is, and light guides the eye. you want the focal point of your image to be clear when you squint. and limit your palettes down - maybe in reality things are all sorts of colours, but if you look at films and comics with good / stylised (same thing to me, but that is just me) use of colour, that isnt the case. colour is streamlined for mood, meaning, and making comprehensive images.

another great thing these concept paintings do is layer up their landscapes to create greater depth, in a more mesmerising way.
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(source, a really great comics workshop)8
this ties in with their use of shading - the foreground is darker, higher contrast, key features standing out against the lighter backgrounds, and the further back you go the lower the contrast and lighter the layer. thats how you get that stunning depth

have you studied these paintings you wanna draw from? made copies? copying an artist you love (AKA transcription or master studies) is the best way to get an understanding of what they do so well

also, research into composition, contrast, and depth - theres lots of great resources out there to help you if you look

ooh i didnt see this bit. paint tool sai is Legit made for painting - while i dont like its brush settings as much as CSP, you can still get great painterly effects in sai. play around, see what you can get - and look up painterly sai brushes, lots of people have shared some great settings.

as far as I can tell you already have a fair knowledge of perspective, and your background is actually very good! like far better than a lot of webcomic with the amount of details and effort you put into it.
By comparing yours to the illustrations, I can see that you are looking at creating more DEPTH, however the quality you are aiming for takes a tremendous amount of time, maybe even more than the amount you've already spent currently, those illustrations are meant to be a one-off piece of artwork and to be honest, background doesn't play the major role in comic, some people could spend a little more time on a panel because of the background but they will move on to the next one, so often some people will feel discouraged because people don't fully appreciate it but it's just the way it is. Yet every comic needs backgrounds.

What I can tell you is that, go easy on it. Invest on about 2-3 key backgrounds for an episode for example. And from what I learnt from Japanese mangaka, you gotta go out and take a bucket load of photos of different locations and at different points of view for each locations, look at them and they will help you visualize the perspective which you can borrow directly from there, then add in whatever fantasy element to suit your need. (if you've already done so, good!)
A tip to create the background like those is maybe draw lineart, duplicate it and lower opacity and then create coloring layers between them so you don't leave outlines but can also see what you're painting over, paint it exactly like you're doing with traditional oil painting (a world different from cel shading)
For the tools to paint I think apart from CSP there's MedibangPaint? it did the job fairly well and easy to use which I have switched from CSP to use it more often.
Hope it helps.

I wish I could paint like those and I'm aiming for Ghibli style straight up traditional.
But from my limited experience with background, try and avoid black outline, and try using color as a way to define the buildings. you have to take account of light and shadows and their strength.
also try to texturing the building with color, like weathering or dirt, decay, colors getting dull from the sun.
when I look at your drawing the characters are swallowed by backgrounds, try to defuse the background so the characters will pop more.
These are some background I did. I'm teaching myself.
hope I helped.

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The inspirational examples you've posted, while amazing, aren't really realistic as comic pages, not unless you're got a big professional team, or are willing to spend 10 years on one short book, or are somehow able to become one of those concept art freaks who can pump out that level of insanity in a couple of hours or less. (and let's be honest if you could do that, you'll probably be better off becoming a famous concept artist).

But having said that, there are creators on this very site putting out mind blowing backgrounds week after week, so maybe looking to their work will give you a better idea of what's possible.

Here are some of my favourites:

But how to get there? There's no way that I know of other than diving into the theory (which you can do easily on Youtube) and just spending thousands of hours honing your craft.

Personally, if I were you, I'd collect a lot of references of the kind of work you'd like to be putting out (again, be realistic, remembering you're going to need to be pumping out work regularly), and just study and emulate what you see.

Hope that helps, and to show you I know a little bit of what I'm talking about, here's a link to my comic, which has lots of detailed background work.

Check out this guy's channel, he also gives classes as well to give tons of information for free. He's amazing and promise, you won't regret it.

Your backgrounds are already quite beautiful but hope he helps you get to the next level, talking about light source, values, textures, etc.

He starts with this video in case you feel lost: https://www.youtube.com/watch?v=x6BlTEytocc&list=PLkii92opOOAvJl8jvvFdJ7UXDFEO5Heic4

What makes a lot of these look good is the composition, actually!! There's a strong sense of foreground/midground/background and good colour/value composition that emphasises the important part of the scene!

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Thinking about the scene in terms of forergound/midground/background can be a really powerful way to break out of thinking of them as "backgrounds" and instead thinking of them as "environments!" I think that when you look at "backgrounds"/environments as simply a backdrop for your characters, it's easy for it to end up feeling flat even when your perspective is good; to feel like the characters are in front of it instead of in it.

This is a real quick scribble so the perspective is obv not perfect, but look how much of a difference it makes to pull the camera down a bit so you can make that fountain a foreground element!

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As far as perspective taking too long: here's a collection of some of my Cheater Perspective Advice9 I shared with a friend once. It focuses on architecture, since that's what tends to be the scariest kind of perspective to those unfamiliar with it, but honestly that sort of "hanging figures on a horizon line" works for anything as a way to quickly get a sense of perspective without going all out and breaking out the rulers.

Here's another example, something I scribbled up real quick to show a friend how I go about building a scene:

I sketch the two figures sitting together, figure out where to put the horizon line (I decided I wanted the buildings to be tall, so we should be looking up from low on the ground), then scribble a rough building to get a sense of where the vanishing point would probably be in that first drawing. In the second one I started adding a couple figures based on where they'd hit the horizon line so that I could get a good sense of sizing for the foreground and drew more of the building based on the rough perspective I've established, and then I started filling in details in that last sketch.

This was drawn very quickly and it's not Mathematically Perfect, but it's close enough and it gives a good sense of depth and feels like a real place -- because it has elements in different levels of foreground/midground/background and places the characters in the environment in a way that doesn't make it feel like a backdrop. I honestly think that's more important to a compelling environment than precision with perspective is!