Strange.

I used IceDragon which is not linked in any way to Instagram to test the link.  Instagram asked me to log in but I just clicked on the X to close the request and the video ran.

The link https://www.instagram.com/surgerymd/reel/C1w4RR2rHAP/  is when I used IceDragon.  The guy cuts wood, rope, tennis balls with his knife and completes a course with knife intact.  I thought it was interesting that he was able to chop so much wood and still able to cut a thick hanging rope.

The other https://www.instagram.com/reel/C31KeXCskZE/?utm_source=ig_web_copy_link  is number of short clips of ads that ran in the 60's and 70's also ran in Opera and IceDragon.  Even my TOR browser that is showing it's location as Poland and never had an Instagram account was able to load the video.

I'm sorry that you couldn't see them.  Who knows.