Since I have successfully watched this video in the past, I decided to try rolling back some of the recent package upgrades I've done, in attempt to see which one broke this.
I've learned that if I downgrade xserver-xorg-video-intel to 2:2.99.917+git20161206-1 (and xserver-xorg-core to 2:1.19.2-1+deb9u8) the problem goes away, and I can watch the video.
The following three combinations of packages trigger the problem:
v1/buster
xserver-xorg-core 2:1.20.4-1+deb10u9
xserver-xorg-video-intel 2:2.99.917+git20180925-2
v2/bullseye
xserver-xorg-core 1.20.11-1+deb11u3
xserver-xorg-video-intel 2.99.917+git20200714-1+deb11u1
v3/bookworm
xserver-xorg-core 21.1.7-2
xserver-xorg-video-intel 2.99.917+git20210115-1
(v1, v2, and v3 differ only in those two packages)
I can go to snapshot.debian.org and bisect between the Stretch and the Buster if you think that would be useful.
More details about my system:
This is a "Mac Mini (Mid 2007)" with a Intel 945-something chipset with a GMA 950 video hardware.
Info gathered by "reportbug xserver-xorg-video-intel" (I didn't actually submit another bug):