Shokz support is fairly unhelpful. They point back to Teams for problem solving as Shokz does not offer any type of firmware update to their devices.
I feel at this point this should be a software fix on the Teams side. I've used my Aftershokz Air headset for years before this became an issue. After a random Teams update sometime in 2022 the headset started the "Mute on" and beeping every few seconds, rendering the headset unusable. I purchased a newer OpenRun to see if the problem persisted, and it does the exact same thing. Luckily the headset was not purchased for use in Teams, but I wanted to see if the problem was still there.
Also, as people have mentioned, the workarounds do not work for all devices.
Holding the volume rockers was a temporary fix, but this stopped working after some time. Now holding the volume buttons together does nothing. Keep in mind the Shokz headset did not change during this time, as there are no firmware updates for the device.
Disabling "Handsfree Telephony" in properties worked for a while, but the headset connected slower and the sound quality degraded noticeably. With the recent Teams update, if you deselect this option, your headset will not show up as a valid "Microphone" option. Also, the "Mute On" and beeping will come back.
If you deselect this option while on a call, you will have the option to use the Shokz headset during the call, but you will not hear anything on the headset.
The last thing I want to mention is if you do have an older Air unit like mine, be sure to unmute before turning off the headset. If you turn the headset off while the headset is "Muted", the mute beeping will persist EVEN AFTER TURNING OFF THE HEADSET. You will need to plug into a charging USB to deactivate it, or switch sources before you power off. This has drained my headset on numerous occasions.