TikTok is a centralised social network and requires the use of proprietary software. It is practically impossible to query TikTok with the browser in a decent way without losing privacy or freedom... unless you use another interface, such as ProxyTok, which I describe in this article.
The ProxiTok interface is simple. You can go to trending content, discover users and search by username, tag, TikTok URL, music identifier and video identifier.
The project was launched on 1 January 2022, so it is quite young and more features are expected to be added. To automatically redirect to ProxiTok you can install the LibRedirect extension, which also prevents other privacy-harmful websites.
There are several public instances, and it is possible to install one on your own server.