So that format of writing is referred to as epistolary writing, where a narrative is constructed out of discovered letters or diary entries, or written to feel like it was, and it's an established but fairly niche way of writing a story.
The problem comes in trying to convey the narrative while also maintaining the illusion that it's an actual diary. What people actually write in their diaries aren't like novels. If someone has a really great day and they write about it in their diary, they may go on and on about their awesome day, or they may just write, "Today was a good day :)" Same with if someone has a shitty day. If something really bad happened, maybe they don't feel like writing about it at all.
Also, when someone is writing in their diary, they aren't going to describe "characters" to the reader. Nobody writes in their journal, "I went to lunch with Dennis today. Dennis is my best friend and we've grown up together, and he has curly red hair and wears glasses." So the reader of your story will probably never get a description of any of the characters in your story, because to the diary-writer these people aren't characters who need to be described, they're just people. The closest you might be able to pull of is something like, "Linda got a new dye job yesterday, and I think it looks like shit. Her faux blonde is so bad, she should sue whoever did that to her."
Also also, when people keep a diary, they don't only write down the things that are important to the "narrative," because they don't have an overarching storyline, they're just writing about their lives. So if you're really trying to make it feel like a journal, then there are going to be entries where all that's written down is what they had for lunch that day, or how they spilled coffee on their new top, or what shows they watched on Netflix that day, which isn't very exciting.
So it's a delicate thing to try to figure out how to balance, making something feel like believable diary entries, while still conveying the information needed to tell the narrative. I suggest reading some epistolary novels to see how they manage to do it. The classic is The Diary of Anne Frank (which has been heavily edited from the original diaries), and I personally love The Perks of Being a Wallflower (which is conveyed through a series of letters instead of a diary, but it's still epistolary and still has those same struggles). The original Bram Stoker's Dracula was also epistolary, and so is The Color Purple.
Be forewarned that not a lot of readers enjoy this type of prose, so even if you do get really good at it, these sort of things are rarely extremely popular. But it's definitely a fun challenge if you want to push yourself literarily!
