[tracking] use `lua-types` treewide

[MattSturgeon]

With #3213 merged, we should start using it. This should be a gradual process, perhaps starting with the settings options created by mkNeovimPlugin.

This issue should add check boxes and/or sub-issues for and identified places where we are using something like types.anything to represent lua. Such cases should all migrate to using lua-types eventually; usually lua-types.anything.

• mkNeovimPlugin's settings option
• (new) lsp module's server settings
• diagnostics, opts, etc