I’m not sure about Proton Pass, but some password managers keep a local encrypted cache of the password vault. If you set your device in airplane mode (no network access) and login you may be able to export your vault.
While no help for you if you can’t get back in, you should always have a usable off-line backup. I use Bitwarden and can directly import a Bitwarden .json file into KeepassXC so I have a ready-to-use backup. With Proton Pass you’d have to export to .CSV then import that (perhaps with some manipulation) into KeepassXC. I prefer KeepassXC because it can run on all my devices and has built-in support for TOTP. Just beware that not all data in your vault will be imported (particularly attachments and passkeys).