Safari on iOS can sometimes be a bit tricky with file downloads compared to desktop, but you definitely don't need to download any sketchy apps from the App Store. When I'm on my iPhone, I always use TikTok Video Download directly through Safari. All you have to do is copy the share link of the video you want, open up the site, paste the URL, and tap download. The video will be saved straight to your downloads folder, and from there you can easily export or save it right into your native Apple Photos app. It's completely free, fast, and doesn't spam you with weird malware.