On that note, Explore API Data for Core Integration · Issue #1 · ClassicPress/Directory · GitHub
The main part is fairly simple. Look at Changeset 50921 – WordPress Trac for the plugins part. This is supposed to be expanded to handle themes also in WP 5.9.
The other part is user interface, where you give the choice to show CP or WP results. That is already handled for themes in Customizer. We can use the same technique for plugins.
Today in WP Slack, a plugin developer asked about shipping updates.
Mika answered:
Adding that to all your plugins would be NOT permitted. Creating a new plugin, as Alan suggested, that is only there to handle updates, WOULD be permitted. However … if by ‘our servers’ you mean WordPress.org, then this should a core ticket. If you mean your own servers for pro plugins, then do whatever you want on the code you don’t host on WP.org
I have concerns about this intermediate limbo state of all the CP plugins doing their own updates.
Speaking for myself, my plugins aren’t submitted to the WordPress Repo, but if a plugin was submitted to the WordPress Repo then I’d have it using their standard update mechanism, which plugins installed on a ClassicPress site would still use.