I have apply-bukkit-default-permissions: true in my Config but the default-permissions doesnt work anymore after the migration from PEX to LuckPerms.
What can i do?

LuckPerms v4.2.42

According to the description does the apply-bukkit-default-permissions: (btw. GitHub uses Markdown in their issues, so [code][/code] won't work) only set, if permissions, that the plugin-author set for default (default: <true/false/OP> in the plugin.yml of the plugin.) should be applied or not.
https://github.com/lucko/LuckPerms/blob/da3c2a073a6bcdd7e29ec7ee2d6546fdc7c21f64/bukkit/src/main/resources/config.yml#L412-L418

I'm not sure, if that really is the case with your issue or not.
Also what "default-permission" do you mean?

Can you give an example, so I can look into it?

Sure, i noticed it with chestshop. In the plugin.yml is the following entry:

  ChestShop.shop.*:
    description: Gives access to all user ChestShop permissions
    children:
        ChestShop.shop.create: true
        ChestShop.shop.buy: true
        ChestShop.shop.sell: true
    default: true

The users couldn't create shops after the migration. When I gave permission to the permission-group, everything went back to normal behavior. It seems to be some other plugins which doesnt work with it.

Thanks, I'll take more of a look into this soon - I'm travelling at the moment, so just have a crappy laptop to work from, making testing things a bit tricky. :)

Only thing that springs to mind is to check for any negated permissions under shop creation.

LP does things a bit differently, and I think a negated permission at a higher level, for example if you negate ChestShop.shop.create - will override the default perm.

Also bear in mind that whilst with PEX, the order of permissions within the file is important, this is not the case in LuckPerms. Permissions apply based on a priority system, which is summarised here. https://github.com/lucko/LuckPerms/wiki/Advanced-Setup#permission-calculation

Were you able to test my suggestion above?

I have a feeling that's what the cause is.

I hope you had a nice travel ;-)
There was no negated permission that i found. I tried some things and maybe i've found something.

That ist our Permissiontree with explicitly set ChestShop.shop.*:
https://luckperms.github.io/treeview/?sLViFczwi2

This is without the permission set to default-group:
https://luckperms.github.io/treeview/?wzpV3joiyk

It seems that it take the parent-permission-node but not the permissions under .buy, .create and .sell when its considered by apply-bukkit-default-permissions

I'm still away, will take a closer look later :)