TV Audio Swap for the Ace is not supported on the Amp, and the Amp cannot broadcast Bluetooth.

https://support.sonos.com/en-us/article/listen-to-your-tv-with-sonos-ace-tv-audio-swap

Supported home theater speakers

You can use TV Audio Swap with the following home theater speakers:

• Arc
• Arc SL
• Arc Ultra
• Beam (Gen 1)
• Beam (Gen 2)
• Ray

I'm really bad at TV advice,,,

I think If you are using the projectors Bluetooth you will need to change the projector settings to not use the Amp as the output.

Might look at any autoplay options too, have the Amp not play TV sound when the TV comes on, only when manually selected.

It is the Sonos application of CEC. If you temporarily disable CEC on the projector, the Bluetooth connection will hold.

Thank you, I am trying to change the audio input on the projector from the amp (CEC) to the Ace headphones (Bluetooth). Before I had the amp, I had a Pioneer receiver and did not have this problem

CEC is a “standard” with very loose standards.  Some TVs allow you to switch between a soundbar and Bluetooth all you like, others always default to the soundbar no matter what you try.  This is why we ultimately recommend disabling CEC to get a stable Bluetooth connection. 

Again, the Pioneer receiver with the same projector worked fine. Even when trying to switch to the internal projector speaker or the optical is not possible. The amp claims the audio input back

As I stated, CEC standards are anything but standard.  Some devices/configurations work fine, others don’t.  Pointing the blame is not really going to solve anything.  Bottom line, if you wish to listen to Bluetooth headphones with your system’s current configuration, turn off CEC. 

Is it possible to turn off the cec from the amp? The projector turns off the sound when turning off arc- cec

It should not turn off the sound streamed via Bluetooth.

Some TV’s and projectors will limit audio format options if CEC (or ‘Anynet’ as SAMSUNG calls it) is disabled. A CEC blocker can work around this, but may introduce some operational annoyances. The blocker will allow the projector to send out its attempts to control everything, but these attempts will not reach the other components. Likewise the other components will not be able to control the projector.

Thanks for all the suggestions. So there is no way to turn off the cec from the amp side.

It’s supposed to turn off the sound to the soundbar. That’s the whole idea behind CEC, when it is off, the soundbar isn’t recognized.  You should still be able to connect via Bluetooth, which isn’t included in CEC.