Electric toothbrushes, shavers, etc are all fine in checked luggage and their batteries are many times larger. There's nothing wrong with batteries so long as they don't surpass a certain size.
That’s because for a period of time they were poorly manufactured and quite literally exploded. Since there were no real brands as they were imported before they became mainstream they just blanket banned them all.
If it's large enough they may pick it up - I wasn't allowed to board a flight once because they found a powerbank in my suitcase.
I got stopped at security and was shown my luggage. After removing the power bank it was all good, luggage was put onto plane and I was allowed to board.
Having more than 100mL of liquid is also not allowed, but you won't get on the no fly list for that. They'll just ask you to throw it out. Not sure about airtags, but it could be the same.
The AirTag uses a primary coin cell battery (aka non-rechargeable) those are generally not prohibited in regulations like rechargeable lithium batteries are.
https://www.tsa.gov/travel/security-screening/whatcanibring/...
FAA says Apple AirTags are allowed in checked baggage
https://www.engadget.com/faa-apple-airtags-allowed-in-checke...