Sorry for the late reply due to my current paternity leave.
Indeed, there are no requirements (explicitly expressed in HIP-5) in terms of sequentiality or simultaneousness of editing the proposal thread for phase 3 and submitting the binding proposal vote on Snapshot.
Theoretically, you could do both at the same time but I would not recommend it. If you do this, it does not allow for feedback time on your phase 3 post with additional information about the implementation details. This means someone could spot a mistake in the implementation details and call for people to vote “No” in Snapshot.
If you give a few days to a week of feedback time on your proposal thread edited for Phase 3, you will be able to get some comments from people and maybe update/fix some details and thus increase your chances of having the proposal passing through when going to vote.
Conclusion: the recommended interpretation is to wait a few days between editing the thread for phase 3 and publishing the binding vote on Snapshot but not waiting that much is not a basis for dismissal.