An e-reading web app support for (at least) epub and PDF files, usable on both desktop and mobile screens, capable of adding and reviewing highlights and annotations. Koobo comes close. But isn't usable on mobile.
And yes I've tried many options, both selfhosted and cloud based.
Why not use a search engine? If it's privacy concerns, ever heard of whoogle? Let's you use Google search without all the privacy risks involved...
It's almost as good to have obsidian with a sync option on multiple devices, but still an obsidian self hosted webapp would be fantastic! I know there is a docker image that offers something like that, but it's a webversion of vnc and a small Linux container, instead of a proper web app.
Again: going with local apps and a sync option (I too use syncthing) is very user friendly too, but I still miss the option to kust browse to my vault from any computer. Log in, do some work and see the changes reflected in my local vaults:)
This, above all other reasons given in other replies.