Add audio commentary to video

This is probably a trivial question, but I want to make sure I’m doing things as intended.
I recorded some game footage with OBS Studio as *.mp4 video, and now I want to add some commentary. Then upload to Youtube.
I’m using Audacity 2.4.2 with Windows 10.
I dragged the *.mp4 video file into Audacity and got the game audio track fine. I added a new audio track in Audacity and recorded my voice in the new track and edited it, so that I’m fine with everything.
Now I want to save my work to the video file.
How do I do this the best way?

Is there a function in Audacity to replace the existing audio track in the video with my mixed audio? Or do I have to export the audio from Audacity and use some other tool to replace the audio track in the video file?

As far as I see it, I should go to File->Export and export my audio to *.m4a (the original audio format within the *.mp4 is aac). Then use a video editor like Avidemux (or just the cli tool ffmpeg) to replace the existing audio track with my newly created track. Is this the correct workflow?

Yes, that one.
On the rare occasions that I do this sort of thing I use Avidemux.