I've migrated several projects from 2.x to 3, one quite large, and I found no issues and no pain.

More, you can migrate a piece of a time, moving each file to be 2/3 compatible without changing anything, and only switch at the end.

I cannot identify one library that works with 3.6 but not with 3.8. More, I can't identify one feature in 3.6 that isn't there in 3.8, and I can't think of one reason why a library written in 3.6 wouldn't work in 3.8.

Can you clarify your post by identifying which features in 3.8 break code written for 3.6, and which are these non-3.8 libraries?