It seems like you then also need to adjust Firefox/Mullvad to remember history and not use private browsing mode, which defeats the purpose of Mullvad / private browsing...
Thanks for reaching out. 1Password's browser extension needs to be able to store your 1Password data on your computer. If “Never remember history” or “Always use private browsing mode” are turned on, browsers based on Firefox (such as Mullvad) prevent extensions from accessing and saving data to the local database, which 1Password relies on in order to function properly.
As a workaround, if you want to use 1Password in the browser while also preventing your browsing history from sticking around, you can set custom history settings in Mullvad (I tested these steps in Firefox but they should be similar in Mullvad):
Open Mullvad.
Paste about:preferences#privacy into the address bar and press Enter.
Scroll down to "Cookies and Site Data" and turn on "Delete cookies and site data when Mullvad is closed".
Scroll down to "History". For "Mullvad will" choose "Use custom settings for history".
Turn off: "Always use private browsing mode", "Remember browsing and download history", and "Remember search and form history".