You might want to look at LibraryThing.
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That's what I use. It works great. No idea if you can host your own though.
I use this app called bookshelf by Damir Juretic
https://play.google.com/store/apps/details?id=com.bookshelf.prod&pcampaignid=web_share
you can scan the barcodes, or even the ISBN text printed on inner cover.
can have multiple virtual bookshelf's to represent your physical shelfs if you like, has a search feature too.
can export and import csv files of the inventory too
no ads and free, I haven't had any issues with it.
Honestly, that seems like a perfect use case for a spreadsheet.
I'm not aware of anything purpose built that does this, but should be pretty easy to build something with Budibase or similar lowcode tool?
If you can be bothered putting in all the ISBNs into your database, it should even be pretty straight forward to implement a bar code scanner to lookup.
Dewey decimal system IIRC from my school librarian days in the 70's. I'd search like this:
https://github.com/topics/dewey-decimal
This might be a start:
There are a lot of apps that do this, not sure about a self hosted web service