In one of our current project, we currently list roughly ~30k items under a single category and it is sometimes a bit difficult for us / the content team to search for products using the backoffice. Our project contains about ~60k products, what's the maximum number of products supported inside Commerce ?
Is there a way to customize the search bar (top left) to search for products using an intuitive way (our editors might not be familiar with search indexes like Lucene) like full text or multiple properties at the same time and display more than a dozen items ?
For your first question, we have customers with a few milions products and it still works fine. the key here is categorization, and 30k under a single category is not the best way to organize it (you still can, however things like UX will be affected)
I don't get the second question - editors should not be concerned about how the search is implemented (indexed search, full text search etc.). True that UI can be improved, but that is decoupled from the search engine under the hood. If you want to, you can implement your own ContentSearchProviderBase to control how the search is performed (for example you want to prioritize the match for certain field). However the way search result is displayed will be harder to change.
Is there some kind of built-in pagination that can be enabled for the backoffice when looking at a large set of products ? If that's not possible is there a plugin doing that ?
For Catalog UI it actually has the built-in pagination - via lazy loading. If you want to have "true" paging then unfortunately I don't know any plugin that does that.