Can headphones (or hearing aides) be used on a 570 or 970 while on a phone call (in lieu of the watches mic and speaker)?

It works similarly reliably as with other Garmin watches that have a speaker and microphone. You won't switch to headphones or start a conversation through headphones if you press the green receiver button on the watch. You can switch to speakerphone on your phone. Unfortunately, modern chipsets in watches work in a similar way. They don't control input/output devices. This also applies to such giants as the Apple Watch or Samsung Watch. I don't know about Chinese brands. Farmon developer once gave me a very detailed answer to this issue. This is a hardware limitation, the shipset doesn't have the ability to switch an external source and control it. The watch is not recognized as a watch then, only as a speakerphone.

If headphones connected to the watch and the watch commented to the phone that had to be nearby, wouldn't it be easier to just connect headphones directly to the phone?

It makes no difference. The watch cannot switch to headphones on the fly. The microphone and speaker are treated as a hands-free set. Both in the phone and the watch. This is a hardware limitation, and Garmin has not invented or does not want to invent another chipset to support the microphone and speaker. So we have to wait and see what the future brings.

Thanks for the info. The ability to use the watch to accept a call (and to then automatically use my hearing aides) is a must for me. Pity because I was waiting for the Elevate 5. So, I will purchase a 265 or 965. Thanks again, you have saved me both frustration and dollars.

You can accept a call on the watch even if headphones are connected to your phone. This has been available even on Fenix 6.

Yes I can accept a call on my current watch and I don't want to lose that feature

It is possible to answer using headphones, if you press the button on the headphones. Then it works bypassing the watch and you talk through the headphones. If you answer using the button on the watch, you will not switch to the headphones. Unless you switch the call to speakerphone on your smartphone. And then switch to Bluetooth on your smartphone. This works differently than in the Epix series or the older Fenix, where pressing the button on the watch or the connection icon, the voice appeared directly on the headphones.