I am experiencing the same issue on a 2015 MacBook Air - I haven't tried with my MacBook Pro yet. Updating my Apple TV now from 14.0.2. I will post if this fixes the issue, but I believe its Big Sur causing the problem. I too do not have Airplay in my Toolbar.
Hope they fix this soon, as I use airplay often.
-- Update
I don't know that updating the Apple TV helped. After the update however I tried this again from the video browser window (On Video Airplay Icon) where it showed two selections with Checkboxes. Clicking on the Apple TV selection didn't do anything, but clicking the Apple TV's checkbox did.
Its working now for me. Now I need to see if I can mirror my screen to the Apple TV.
dkalbach
Users receive reputation points by contributing quality content to the forums.
Posts include post and replies published on the forums.
Post authors can mark replies as Accepted to indicate successful solutions.
Apple Developer Forums admins can mark replies as Apple Recommended to indicate an approved solution
Last seen
User for
From
Reading, PA, United States