What do I need to apply for an extension of my Thai Non-O visa while staying in an Airbnb?

The TM30 is technically your host's job, not yours. Under Section 38 of the Immigration Act, the house owner or landlord has to notify immigration within 24 hours of you moving in, using form TM.30. They can do it in person, by registered mail, or online through the Immigration Bureau's TM30 system, and they get a receipt slip back as proof. Ask your Airbnb host for that slip, or point them to the online option.

If they still won't do it, the cleaner route may be to apply from your next address once you move, as long as there's time before your current stay runs out. Extensions are handled by the immigration office covering the area where you live, so it helps to apply from where you'll actually be.

As Brandon asked, the document list depends on what your Non-O is based on. For retirement it's the TM.7 form, a passport copy, and either the bank letter plus bank book or proof of income.

Just go ask your immigration office what you need since they all aren’t alike

Non-O visa based on what? You'll most likely need a TM30 that your Airbnb host files. They're legally required to file this but many do not because they don't want the government to know they are renting for income.