I'm sorry, this might not be specifically a LuckPerms issue, but I do need help.

Issue: Players are shown suggestions for commands they don't have permissions for. When they start typing "/", they get 3 suggestions for all plugins. I'd like to know how I can make it so players are only shown suggestions for commands they are able to use.

Running Paper 1.15.2
Thanks in advance.

This is - as you mentioned - not related to LP.
The issue is, that the plugins themself don't properly handle the commands (e.g. assigning a permission to the command through the plugin's plugin.yml) or similar.
A relatively good plugin would hide the command, when you lack the permission, which is a bit rare tho.
A solution for this would be to use a plugin that blocks the command suggestions if you lack permissions.
I can't suggest any specific one, but I'm sure a quick Google search can help you ;)