CKEditor4's image upload has a "Browse Server" option, and when clicked, it integrates with CKFinder to let the user pick images from the file library.
An example is at https://ckeditor.com/ckeditor-4/demo/#document (attached recording of the behavior below)

I've not been able to find similar functionality in CKEditor5. Any help greatly appreciated!
Are you looking for exactly the same "Browse Server" button (and an Image dialog) in CKEditor 5 or are you looking for the functionality to "browse server" and insert/reuse images using a file manager?
CKEditor 5 comes with two solutions that provide this functionality:
CKFinder
CKBox
(You may expect CKBox to come up with new features soon, such as: private files, workspaces and image editing)
Due to how the CKEditor 5 image feature has been implemented, opening "file managers" is available done via a separate, dedicated toolbar button.
Could you let me know if this is what you are looking for? Or would you like it to be available in a different way? If yes, then could you elaborate on why?