Display name, username and bio on TikTok
TikTok has two names. The username is your @handle and the link to your profile; it only takes letters, numbers, periods and underscores, so styled letters are refused. The display name is the larger name at the top of your profile and next to your comments, and it accepts Unicode, so that is where a styled name goes.
The bio is 80 characters, which leaves room for roughly one line of positioning and one call to action. A styled first word or a small caps tagline gives it some character; keep the call to action plain so it is easy to read.
On-video text versus caption text
Text drawn on the video and text in the caption are two different things. On-video text is part of the picture and uses the styles in TikTok's editor. Caption text is searchable text under the video.
That difference decides where styled Unicode helps. On the video, it adds looks the editor does not offer. In the caption, use it sparingly: the words in your caption help TikTok and viewers understand what the video is about, and styled letters are not read as those words. A bold first line followed by a plain caption and plain hashtags keeps both benefits.