When I wanted to do exactly this I used Calibre2opds. I keep my Calibre library in my Drop Box folder. I then use Calibre2opds to create a sort of web-based catalogue of it. I now can use my kindle iteself to browse the library, but author, genre, newly added titles and so on. I just worked (slowly - I'm no techie) through the instructions in the thread at
https://www.mobileread.com/forums/showthread.php?t=64095 You end up having to run this to create the webpages. So I do it after any significant additions to the library. I suppose that could be considered tedious but it seems OK to me.
And once the library was being stored in Dropbox anyway I've switched to using the portable version of calibre so my calibre settings are all the same whether I run it at home or at work.