Out of curiosity I used Siri on my Apple Watch Series 3 (non-LTE, as Apple does not support that in my country) to find my AirTag (that I left at home) during an MTB ride. I was surprised to get an error message that I cannot use this watch to find objects; I should use an iPhone instead. The watch is paired to my iPhone which I was carrying along (for Strava beacon; which works fine).
Can’t you use a (non-LTE) Apple Watch with AirTag (tethered to an iPhone)?