I have the gamepass version. The kits only work when the team was licensed in-game, such as City and AC Milan. If the team is not licensed, the new kit just will not show. Any tip on how to fix this?

Is your game installed in C drive?
With Gamepass, folders  are a bit different..try to put a couple of kits here:

C:\Users\**youraccountname***\Documents\Sports Interactive\Football Manager 2023\graphics\kits

Then in game, under Preference - Advance - Interface - scroll in the middle where it says "Reload skins when confirming changes in Preferences", hit “Confirm“ and it should load the graphics..

You have to create the folders you don’t have in that path

It's weird. I tried to do what you did and the results are exactly the same: teams that are licensed (Man City, for example) get their custom kit applied correctly, while not licensed teams (Man United, for example) do not. It's weird, because there seems to be some problem with licensing blocking the kits getting applied correctly.

Did you enable the possibility to have mod in the game?

If no, open XBOX app then go to game's page. There, you have to click on the three dots button next to the “add to play later” button. Then click to Enable Mods option.