Re: "How to connect airpods ( 3rd gen) to apple account but not connect via bluetooth via iphone/mac"
Seems AirPods are an accessory of the Mac or device they are paired with.
Set up Find My on all your devices - Apple Support
says:
Set up your AirPods
If you pair your AirPods with your iPhone, iPad or iPod touch, they show up in your Devices list in the Find My app. You can use Find My to locate or play a sound on them. If your AirPods support the Find My network, you can also mark them as lost.
For more information, see
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What to do: If you get an alert in the Find My app that your AirPods setup is incomplete - Apple Support
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If needed: AirPods Support Website: (info. / support / contact options etc.)
Find all the topics, resources, and contact options you need for your AirPods....
AirPods Support - Official Apple Support