The president does not have broad authority under IEEPA.
Congress specifically limited presidential authority when passing the act, and TikTok is protected under IEEPA 50 U.S. Code § 1702(b):
> The authority granted to the President by this section does not include the authority to regulate or prohibit, directly or indirectly - (1) any postal, telegraphic, telephonic, or other personal communication, which does not involve a transfer of anything of value; ... (3) the importation from any country, or the exportation to any country, whether commercial or otherwise, regardless of format or medium of transmission, of any information or informational materials, including but not limited to, publications, films, posters, phonograph records, photographs, microfilms, microfiche, tapes, compact disks, CD ROMs, artworks, and news wire feeds.
https://www.law.cornell.edu/uscode/text/50/1702