- Edited
Looks like it's all a bit fuzzy but 100 GB seems to be the hard cap for GitHub repository sizes although GitHub advises to keep it under 1 GB and may send a notice when getting over 5 GB (but it sounds like you can talk to them about it). And 100 MB is the maximum file size you can upload.
All of this is for free repositories. I have no idea if things change if you have a paid account.
GitHub supports Git LFS though, so that helps a bit when working a lot with bigger files because Git isn't really a good option if you have big binary files. Git was made for text diffs after all.
And that's why a lot of game developers don't use Git for their projects but for example Perforce instead. And also why they don't use GitHub but host their repositories on their own systems. Games are big after all and for non-hobbyist games GitHub will eventually get too limiting.