I would run a packet capture while using TikTok from both mobile and desktop and then review the host names and IP addresses used so you can create some rules to block those specifics. It may not be perfect, but should do the trick with some possibility you need to revisit again if they change some things.
I have been trying to figure this out for a while also. Based on the yelling from my 14 year old son that Tik Tok won't work I on his Iphone, I finally got it right when I added these to my firewall rules.
Is it still blocked for you? I blocked no fewer than the recommend domains and IPs and network ranges and, although the site fails in browsers and the Windows desktop app, the TikTok phone app still works like a (cursed) charm. The worst part is having to expose myself to TT crap with every test.
its doing it all now. these 3 entries seemed to make 99% of the videos fail. some of my coworkers use the app. i let them test it for me, the rest of us refuse to install it, treating it like a suspicious link no one wants to click lol. the 3 entries have not prevented the app install or opening, but the videos fail to load.