I think https://mymind.com/ might be trying to build what you are looking for, I didn't use it myself, but I read around that the auto-categorization and content-search are not so great though.
I personally use manual tags to organize my bookmarks as I find them easier to maintain than a very rigid hierarchical folder structure. I also find that having to force yourself not to create too many tags is helpful rather than disruptive.
About the "I wonder if I should write it myself" it seems that the bookmarks app space is quite crowded so I guess it'd depend on what you'd like to achieve with the project. I ended up building https://www.keepalink.com if you'd like to give a try to using manual tags with minimal friction. This is a very young project and I'm not sure if it will support automatic tagging and content search at some point though (which seems more in line with what you are looking for right now).