How to recover data from locked Apple-silicon Mac without recovery key or Apple Account?

I may be able to help you understand what's going on, but recovering data is a completely different subject altogether.

The bottom line is that (like everything Apple does) a Mac and its systems are fortified against unauthorized intrusion to the extreme that it makes data recovery from a system that does not recognize authorized access effectively impossible. That leaves only the affected Mac's Time Machine backup (or some third party backup solution) as the only likely source of recovery.

I'm going to lose a lot of data.

One should never be concerned about losing data. Time Machine has been incorporated in Macs for about two decades: Back up your files with Time Machine on Mac - Apple Support. If the prospect of losing data gives you the slightest concern, you need to reevaluate your backup strategy.

Why it happened: The most likely explanation is that the MBA's built-in storage suffered from some unknown corruption that rendered its login credentials unrecognizable. Obviously that should not happen, and the cause may never be known, but the fact is all sorts of things in the material world fail for all sorts of reasons. We hope they don't, but hope is not a contingency plan.

The only occasions in which I have been made aware of that problem is spontaneous startup device failure. It manifests in the symptoms you describe. You did nothing to cause it.

There have been occasions in which forcing the Mac to shut down then starting it up again in the usual manner resulted in login success, as though the prior experience had been nothing but a bad dream.

Apple's guidance on the subject is both cursory and longwinded, but it's all we have to work with:

If you forgot your Mac login password - Apple Support

"Restart your Mac" is the bad dream I alluded to. Sometimes, it just works. Then, we redouble our backup strategies 😄

To restart your Mac, press and hold the power button or deep press the Touch ID button and hold for more than ten seconds.

To me it is sounding like you may be confusing an Apple account password and a computer user password. When my Mac starts it only wants my computer user password.