Would it be possible for LuckPerms to change a person's nametag (name above their player head) to their primary group's prefix / suffix on login? That way if their primary group's prefix color is blue, the nametag above their head can also be blue. Or would this be too far outside the scope of LuckPerms due to complications with scoreboards in 1.13?

I'm coming off from the plugin ColoredTags. This worked beautifully with LuckPerms and matched the player's primary group to a group configured in the plugin. So if a player changed their primary grouping in-game, they would get assigned the new prefix/suffix to a matching group automatically. It also worked perfectly with the Paper (Spigot fork) setting where you can disable player collision - which forces players to a scoreboard group without collision enabled. Unfortunately this plugin no longer works with 1.13 due to game changes.
https://dev.bukkit.org/projects/colored-tags

Testing out a similar plugin which has been updated for 1.13, NametagEdit, this plugin unfortunately does not auto assign nametag groups to players with matching primary group names. You are forced to assign a prefix/suffix with permissions, which does not work well if a player has multiple groups which inherit a nametag permission. In other words, players who change their primary group can't get their primary group's nametag above their head. It is also not compatible with Paper's auto-assigning / disabling of collision.
https://github.com/sgtcaze/NametagEdit

I found an alternative plugin that does seem to work with the primary group!
https://www.spigotmc.org/resources/tab-1-8-x-1-13-1-reborn.57806/

This suggestion doesn't have to be implemented into LP.