After scouring through the entire web for close to 5 years and giving up out of sheer frustration every time, I was finally able to upload my TeX sources to arXiv (as of 17.01.2024). The solution was buried as a comment to one of the lesser upvoted answers in a less popular StackExchange thread. I hope Google will push this post high up so that it can help Overleaf (and minted) users.

1. Compile with \usepackage[finalizecache,cachedir=.]{minted}
2. Go to logs and output files > other logs and files and download everything with pyg. (all the *.pygtex and the *.pygfile)
3. Compile now with \usepackage[frozencache,cachedir=.]{minted}
4. Download the complete project .zip by submitting it to arXiV
5. Unzip and put all the *.pygtex files and the *.pygfile into the folder
6. Zip again and upload to arXiv; Works for me!

Answer source (User: rhombidodecahedron)