@GijsGroote Welcome to the forum!
I’m not sure if resurfacing a 2-year old thread was your intention, but regardless, the answer provided by @djsmith85 in 2022 is still accurate.
It seems that you may not fully understand the distinction between logging in to a logged-out extension vs. unlocking a locked extension — in Bitwarden, the distinction is important (see explanation here).
The most common (and recommended) usage of Bitwarden is to keep your Bitwarden client apps and browser extensions logged in, and to lock them when not in use. If your vault is locked, and you need to unlock it, you will never be asked to enter or confirm your email address. This is what it looks like in Firefox:
You also have the option of unlocking using a PIN or biometrics instead of your master password.
If you need help with configuring any of this, or have additional questions, I would suggest starting a new topic in the Ask the Community section of the forum.