To echo others here, Clip Studio new page presets (like their A4 page size) are usually set at a decently high working resolution (dpi) by default. The defaults are usually either 350 dpi or 700 dpi. I'm not sure why it's not 300 and 600, but Clip Studio does what Clip Studio does. Anyhoo, a 700 dpi working resolution will produce that 6000+ pixel size you're seeing on the A4. Good news is, you can export the image with a lower export resolution without changing any of the original images settings.
The linked guide page is a little old, but looks to have the appropriate options for the export feature:
Clip Studio Paint User Guide
Option 5; Output Size, can change the image output size in 3 different ways: (1) By Ratio, (2) By a specified output size (already mentioned) and (3) By a specifiied resoution; this is what I use. I just set it to 96 dpi and that 6000+ pixel width becomes the 700-800 pixel width you're after.
Like others have also mentioned, you should work in as high of a resolution as your pc can handle. The 700 dpi default should be fine though. Personally, I run it down to 600 dpi, because I've worked with 600 dpi resolution forever and I don't like change, LOL.