I have been trying to find how I can view the subdivided wireframe that you do in your video. I also read all questions and found that Bill Slobotski (botski) asked the same question back in 2018, so I tried his solution going into object mode and then putting my viewport shading to wireframe, but that did not help sadly. I would be thankful for an answer to this question of mine.
Best regards
Daggismaggis
In the Viewport Overlays you can enable Wireframe:
You can also enable Optimal Display in the Subsurf Modifier.