I think most likely Apple and Google will have to remove TikTok and WeChat from the app store in U.S. If you install manually on Android you would probably be able to continue to use it. The executive order only bans transactions (since that is the limit of the power granted to president by IEEPA), so the executive has no authority to "block the app at the network level" -- the IEEPA explicitly restricts the prohibition of "any postal, telegraphic, telephonic, or other personal communication, which does not involve a transfer of anything of value".
AFAIK the term "transaction" comes directly from IEEPA since that is the law that lets the president make this executive order, so if you want more details on what is included in "transaction" you can see the text at https://www.law.cornell.edu/uscode/text/50/chapter-35
If transaction refers to a payment transaction, then I don't understand how this isn't an abuse of power if it leads to removal from app stores, thus removing all functionality. If the president has the power to ban financial transactions, fine, but by effect, if the app is then removed from the app stores, then that effectively bans it for any other use as well, such as text, video chat, and audio calls, which is against the restrictions you quoted.
If I travel to China while this ban is in place, am I allowed to use the app while in China (assuming it's not removed from the app stores)?
This is all such a slippery slope. I am just so scared about my family's future. Trump is keeping my family outside of the country, needlessly, and now he is preventing effective communication.
You're right in that (at least under IEEPA) the executive order doesn't seem to have the authority to ban free usage of these apps. In fact it also excludes regulation of "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" (which include films so may include video clips as well).
So maybe the implementation won't be a complete ban from the app store, and instead something much smaller scale that only prevents payments, or if app stores are asked to ban it, maybe the courts will strike it down.
AFAIK the term "transaction" comes directly from IEEPA since that is the law that lets the president make this executive order, so if you want more details on what is included in "transaction" you can see the text at https://www.law.cornell.edu/uscode/text/50/chapter-35