I actually wrote a JS-based encryption container which passes these requirements (and does not even have PasswordSafeV3's key-reuse problem!) for these very reasons about 2 years ago, and one of its example applications in the repository, 'tagaloop', can function as a password storage container:

https://github.com/drostie/nermal

Tagaloop does not time-out or re-authenticate for you, and since I'm not selling the service I can't offer 2FA, but of course if you wanted to build a company out of this stuff it's open-source. In addition nermal makes the deliberate decision to not support "seek" operations, so it does not e.g. store a header field which could then be scanned in advance to index a bunch of concatenated binary strings -- this is not bad for password storage where the metadata outnumbers the data by a factor of 2 or 3 so there's no point, but other applications like storing an encrypted archive of files might suffer.