A “rescission act” would actually Be in the form of “special request” from the President per 2 USC 28E or 284 detailing the appropriated amount. I see no reason it would not apply to items funded by the omnibus. Key is to make such requests particular as only one bite at the apple. If request fails can’t make another request against a budgeted item that has a prior failed request.
For example go after planned parenthood in one request. Go after funding for hermit crab studies in a different request