Assuming a private plugin, not available via the repository, there are several search results for ‘wordpress private update’ that might be helpful.
In fact, I recall doing it once several (many) years ago, but can’t find how I did it. (And I seem to recall posting the answer here on SO, but can’t find that either.)
But, one of the search results is here https://rudrastyh.com/wordpress/self-hosted-plugin-update.html . The process is a bit complex.
I have a few private plugins that I have written that I use on the sites I manage. But since I wrote them, I know when they change, and I manually update on the sites I manage. They aren’t anywhere else, so don’t have to worry about any automatic processes.
If you are looking for a plugin that will update other sites, there are a few that already do that. But they require their plugin on the additional sites, to provide an ‘authentication’ to the admin area of that other site.
One I use is “Infinite WP”, which is a manager for multiple sites. Each site has their plugin installed, and then the ‘master’ site accesses those sites (via the plugin) to perform updates and other functions. Works quite well.
If you are looking for a way to ‘enumerate’ plugins on another sites that you do not own or manage, then that sounds a bit ‘black-hacky’, and I can’t help you there.