Does macOS Big Sur have screen a Screen Recorder like the previous versions?

Yes. See information in: How to record the screen on your Mac - Apple Support

Yes.

Either use Quicktime Player: File->New Screen Recording; or just press Command-Shift-5, select the button to record the whole screen or a portion of it, and click Record. And, of course, you can record sound at the same time.

jeffreythefrog wrote:

Luis Sequeira1 wrote:

And, of course, you can record sound at the same time.

?

i thought we still needed additional software, such as BlackHole, to record the mac's internal sound. has that changed?

No, that has not changed. To record the sound output directly you do need BlackHole (or Soundflower, though, since it has not been updated in years, BlackHole is what I recommend now).

My point is that you don't need additional software to record sound from the built-in microphone or any other sound input source.

I added my comment above because a few times people have wrongly stated in this forum that you "Quicktime Player can only record the screen with no sound", or something to that effect and I wanted to make it clear that this is not the case.

Luis Sequeira1 wrote:

And, of course, you can record sound at the same time.

?

i thought we still needed additional software, such as BlackHole, to record the mac's internal sound. has that changed?

oh, ok. thanks for the clarification.