With TikTok, if you copy and paste the URL into a browser you will get a link you can then copy and paste without the baked-in tracking. You can probably do the same with Instagram, but I just got a link from them and they had the tracking under a query parameter (that's the technical term for the stuff after the question mark). So I'm not sure what you're seeing.
Also, thank you for stripping tracking data off of links you share. "It ain't much, but it's honest work!"
https://www.tiktok.com/t/aaaa becomes https://www.tiktok.com/@someuser/video/111 (manually remove tracking as before). I assume this might work with Instagram, but like I said, when I try it, it doesn't actually give me that style URL.