What are the current rules for extending a Non-O visa in Thailand if my passport expires before the extension period?

Even if it was an immigration officer at your immigration office who told you that, it was bad info. It's been at least 3 years since they changed the rules.

Before (as in years ago) you could get the entire year stamped in a passport even if it was expiring and then when you got a new passport they moved the extension stamp.

THEN

they went to stamping you in on an extension ONLY until the passport expired and when you brought in a new passport they moved the stamp and gave you the rest of the year extension for free.

THEN (as of a couple 3 years ago)

they went to stamping you in on an extension until your passport expired and then making you apply for a whole new yearly extension (by meeting all the requirements again and submitting all the paperwork again) when you got a new passport.

Unfortunately you were told BAD info.

If you applied for a year extension with a passport valid less than a year you would get the extension until the passport expired AND sadly for you, then you would apply for a brand NEW yearly extension once you got a new passport AND the extension stamp in the old one was running out.