The thing is: To be able to export your data you will have to enter your password. So that will not work if you do not know your password.
My recommendation would be to keep on using both phones for now. Whenever you need something from inside the old Bitwarden account, then add it to the new Bitwarden account on your new phone. After that is done use the data from inside the new Bitwarden account where ever you want to login. This way you can be sure that the data in your new account is correct.
For the future:
Write down your master password and store it in a secure place you will actually remember. Like in a safe at home or a safe deposit box in your bank - if you have one - or perhaps with your vaccination card.
Also: Type in your master password every once in a while. The perfect moment for this is when from now on you make regular backups:
The official help for making a backup:
And here are some great insides about this topic: