Hi again. Yes you are correct, your old computer could record a new movie and new screen recording because it used the internal microphone as a sound source which picked up sound from the built in speakers, plus everything else in the near surroundings. If you turned the sound/speakers down or off, it recorded no sound from the screen video.
You new flash iMac like mine, is no different. They also record sound generated from the internal speakers. You could set it up by choosing internal mic and built in speakers in the record window menu, which you have located from your comments above.
You could continue to use this method but the sound quality is so poor and so full of artefacts, that most people don't bother.
OK if you are doing a face and voice capture in a new movie recording but if the video is streamed like youtube or webinar, you want the best possible sound source.
To achieve this sound quality, you need to download a utility called soundflower which you have discovered in your google researching.
There are two: Soundflower, you will need to google it, or iShowU Audio Capture. I would strongly recommend the latter. https://support.shinywhitebox.com/hc/en-us/articles/204161459-Installing-iShowU-Audio-Capture. Download the Mojave version as it is for Catalina as well. Download and install, then restart your Mac before opening any application..
Check System prefs / Sound and check that you can see, Internal Speakers, Internal Microphone and iShowU Audio Capture.
Now this is the tricky part, ready?
Locate and open the video you want to play. Play a little to confirm video and audio is OK.
Go back to start of video clip ready to play either stopped or in pause mode.
Open Quicktime Player / File/ New Screen Recording.
A small window will appear with a red button. Next to the button is dropdown menu arrow. Select iShowU Audio Capture.
Go to system prefs/Sound and click Output. Select iShowU Audio Capture. Don't worry about Input Button. Default "Internal Mic'.
Click the record button and you will be asked if you want to record the whole screen including desktop. You usually don't want it so place the cursor arrow at he top LH corner of the window you are recording, click and hold and drag it down to the bottom RH corner or the area you want. A small window will pop up (Start Recording). Press it. Now quickly go back to the window you are recording and press play. The video should start to play.
When the recording is finished, click the stop recording button Top of screen, RHS in the menu bar next to the WiFi symbol, or thereabouts.
The recorded window will appear so you can check it. Now the trick that everyone forgets. Go to system prefs/sound, click Output and select Internal Speakers so can hear it. REMEMBER! Output on iShowU Audio Capture to Record and Internal Speakers to play and hear it.
The only negative side to this method is that you can not monitor/hear the sound as it is recording. The trick is to set the speaker level to above 50%. You may need record a little bit and experiment to see what settings are best for your set up.
There is another utility which is far more complex but gives the ability to run multiple inputs and monitor video and audio levels but that is another story. Achieve what you can with this setup and don't be afraid to ask if things don't work.
Good luck and keep safe.