I have been using and am happy with SafeInCloud
It's not open source, but there is no online subscription - online storage is your choice of DropBox, Google Drive, or a couple others. You can also use your own WebDAV server if you want. The mobile app versions are around $5 at whichever app store (with the occasional sale). There are Windows and Mac desktop apps that are free.
However, I can't speak to its browser or automatic password fill-in integration (which it claims to have) as I have never tried those features.
You can try the Android or iOS app free for a couple weeks.