I have a Mac Studio M1 Max.
What finally worked for me after mutiple searches for possible solutions, huge frustrations booting and rebooting, being locked out over and over, and trying different options, was (it seems!) a new keyboard. Someone else here mentioned keyboards as a possible culprit. I found this during a search: “older Apple Magic keyboards (or other Bluetooth keyboards) can be unable to use certain keys during password entry."
My new Magic Keyboard arrived two hours ago (I hate to thank Amazon but I was so happy for next-day delivery) and hooked it up via a USB-C cable -- one end into my Mac Studio and the other into the keyboard. I also read that the keyboard must be wired.
I had tried to get into Recovery mode before but it never went past the initial screen, nor was I able to get on using my Apple ID since the "@" symbol on my old keyboard did not work. Now I was able to use my Apple ID to log on and when I clicked under the Option box in Recovery mode, it went to the page where you can select whether to wipe the computer, re-install Tahoe, etc. -- as opposed to kicking me off and sending me back to my home screen as it had done before. I clicked "reinstall Tahoe" and hoped. I was prompted for my computer password during installation. I entered my old password and IT WORKED.
I am typing this on my Mac Studio now. Tahoe 26.0.1 is now reinstalled and I did NOT have to change my password. I have not tried to shut down where I would need a password to restart, so I do not know if this will continue to work, but right now I have my new keyboard attached to my Mac Studio and I am hoping for the best.
Also, I read there were issues with FireVault compatibility (“It appears to be related to the new OS's APFS driver no longer fully supporting the old software-based FileVault”) so I turned that off too just in case.
I hope my fix works for others! I was just so happy I did not have to wipe my hard drive and start over. I hope this was not a ploy by Apple to sell more keyboards.