My MacBook Air doesn’t prompt reset password after 3 wrong attempts
I have forgotten my password to my MacBook Air but when I enter a wrong password three times I do not get a prompt to reset it
Question marked as
If you forgot your Mac login password - Apple Support describes what to do. If necessary, proceed with If you can't reset your Mac login password.
Follow all those steps all the way through to their conclusion.
Most of the initial steps begin with "If you see this option... " or "If you are asked for... <something>" because different password reset options have been introduced over the years. From what you describe, at least some of them are not applicable to your Mac or your User Account, or you already determined they aren't getting you anywhere.
Proceed with the steps in that second Apple Support document — the ones that begin with "Start up from macOS Recovery" — and let me know how far you get. Most of them also begin with "If..." for the same reasons.
If (see what I did there?) you ultimately arrive at the last and final steps they describe erasing the Mac, followed by restoring its content from a Time Machine backup.