Just the sequences, ScriptSigs, input index, and the input count are committed to. So if you have an “offer” branch where funds need to be added, it can bind to a payment to a particular user.
But if the other input is a p2sh or legacy, the commitment to scriptsig containing a signature will commit to the specific inputs.
So if you gather the signature, e.g., using ANYONECANPAY, then you can get it to work because you avoid the hash cycle and commit to your input and can form a CTV, the CTV would be able to commit to the other inputs.
This is a bit better than using a signature for presigning, since there’s no other way to spend once it’s in CTV.