I feel this item should be merged with the desktop feature request. I would hope that offline access in the desktop app would be table stakes. If and when that comes, wouldn't that resolve this issue? A fully native desktop app can handle securing your data for better than a browser extension can and would be accessible at all times. Then sync deltas when there's an internet connection.

Why is there an ask for offline access with a browser extension?

I am agree with Henry.

Here the problem is with the browser extension, which requires a constant connection to show data.

In my case, the problem is also due to the fact that Proton is blocked in the country where I am now, because of this, the extension simply shows an error, I have to turn on the VPN every time so that the data is loaded and the extension works for a while. But it's difficult, because for work I have to use VPN to the office, which does not allow me to connect to proton servers (two VPN can't be enabled at same time)

I'm pretty sure this is already how the vault works. Unless I'm missing something. I did the same thing as the other comment state. It opens just fine without an internet connection.

----UPDATE----
Definitely does not work on desktop.
The desktop browser extension logs in to your account every time you open your browser.
This is a massive issue if your phone is not available. Even worse if it is and you have a massive password or secure note that's a pain to type in.

(I recently made another post about a self hosted option - ideally these all follow the same idea - we need offline access to our passwords - I shouldn't have to open my browser JUST to access a password. Many passwords and things are used offline or via LAN. (GPG keys, SSH keys, general notes, etc)

Does this not work already? I just put my phone in airplane mode and I was able to open Pass and see my vault.

Just wanted to emphasis about being able to have a local vault in the phone/computer to be able to access passwords offline.

The vault should be super heavily encrypted in the local unit and as soon as internet is available synced with your servers. This local vault might be an option and not default so people can store it locally if needed but keep it safe with you on your servers.
I just know when traveling the world I often end up without internet and still need something stored in the password manager like a note, card number, membership and other things I like to keeps in a safe place.

One could select parts that would be stored in the local vault. Like if I want my notes, Membership info to be available offline I could choose that in the app settings. The rest would be safely stored online safe on proton servers.