You should be able to put the CSS in the Page Settings under Advanced > Header Code Injection. Just remember to put the CSS in between <style> </style> tags.
However, Squarespace should now automatically display the TikTok icon (I know it didn't originally) so it might be worth removing and re-adding to see if that solves the problem. I added your account onto a cover page and it worked for me.
katycarlisle's post in Custom CSS only working when open on squarespace editor but doesn't show on website cover page was marked as the answer
