Update: this was kinda driving me insane again and I was about to write a bug report, but thankfully I didn't have to, because I found out while I was writing and doing some digging, that an option for this exists already! (oopsie)
Go to:
Settings > Configure Kate > Projects > Session Behavior
And check the box for "Restore Open Projects" to enable it, now when you reopen a session that had a folder opened in it, the folder will show up once again in the Projects view.