There’s already been PRs for language pack (On phone but will try and dig it out in a bit when home). It depends if you do package installs or all in 1 (both should work).

Yup sounds like it should be added to the pack - I think site and admin are currently separate installs in the package? But whichever way should be treated same as site and admin are now

I think we just need to add #__extensions entries to installation/update SQL.

Yep, admin and site are separate "extensions", usually installed with a package. So the api would ideally be a third extension within that pack. Looking at the files, the needed XMLs are already present.
It needs to be added to the package (https://github.com/joomla/joomla-cms/blob/4.0-dev/administrator/manifests/packages/pkg_en-GB.xml) and as @SharkyKZ wrote to the #__extensions

IF that's the way you want to go forward I can do the PR

I haven't thought much about it yet, but I'd say it's the simplest approach. If you can do the PR, that would be appreciated.
Just saw Crowdin needs some adjustment in https://github.com/joomla/joomla-cms/blob/4.0-dev/crowdin.yml as well so it picks up the new XML files.

https://github.com/joomla/joomla-cms/blob/4.0-dev/administrator/manifests/packages/pkg_en-GB.xml

api in here too

are you sure crowdin.yml needs updating? I can see the api on line 15

PR at #28282

@brianteeman Crowdin has the ini files but not the xml files

ah