pairing apple tv remote with bose speaker

What is your model remote? Identify your Apple TV remote - Apple Support

Does you Bose speaker/audio system have an IR receptor?

Program your remote for volume - Control your TV or receiver with your Siri Remote or Apple TV Remote - Apple Support

Neither the Apple TV box nor the speaker would know about Big Sur, nor change anything because of Big Sur.

The Siri Remote would do volume control to the TV or audio system directly, unless you have an AV receiver that can handle volume control over HDMI-CEC, and the Remotes setting on Apple TV is set accordingly.

When the Siri Remote does volume control to the TV or audio system directly, then the Siri Remote uses IR (not bluetooth) to send commands to the TV or audio system. This requires line of sight between the remote and the IR receptor.

If your speaker is a bluetooth speaker or AirPlay speaker, connected wirelessly directly to the Apple TV box, then you would use the on-screen volume sliders in Control Center﹥Audio Controls on Apple TV.

If your speaker is a bluetooth speaker or AirPlay speaker, connected wirelessly directly to the Mac, then you would use the audio controls on your Mac.