Put simply, Whenever somebody logs onto the family computer that I manage, I get bugged about updates and "could you install x thing that I saw in the store" and such. How would I enable all users to run flatpak, snap, and plasma-discover without root? All questions about this that I have seen previously seen only cover running one command without root access. How to run a specific program as root without a password prompt? does not answer my question as it addresses allowing a user to run a single program without root access.
You can use
sudo for that. You can specify what users are allowed to run commands, what commands can be executed, and whether to ask for a password of not. See the manual for details.
If you don't want to that users have to type
sudo in front of the commands, create aliases in
/etc/profile for the commands that will run the commands with