Updating BIOS on 12th gen FW13 running Linux (Mint) -- where we at?

I want to get the 61wh battery. There is frankly a soup of information (forum posts, official statements/articles) on updating the BIOS for 12th gen Framework 13’s running Linux. My current BIOS version is 3.05 based on output from the recommended ‘sudo dmidecode -s bios-version’ command in the terminal.

a) Can I even update this?

b) If yes, what guide should I follow as a normie who needs his hand held?

Thank you