Does Persona-non-Grata apply to embassies' physical premises?
It affects "diplomatic agents", it does not affect "premises of the mission".
It applies regardless of the location of the "diplomatic agent": whether or not within any "premises of the mission"; whether or not within the receiving State.
Does [the] Vienna Convention's Article 22 prevent [the persona non grata] process from affecting the embassy grounds?
The persona non grata process affects the status of "diplomatic agents", it does not affect the "premises of the mission" (e.g. embassy grounds). Nor is this process restricted or impeded by the location at any time of the diplomatic agent in question.
The persona non grata process described in article 9 applies to "diplomatic agents" in a "receiving State" or not. Embassy grounds are territory of the receiving State but the process does not require the diplomatic agent to be anywhere in particular.
Article 22 restricts agents of the receiving state from physically entering the premises of this mission without permission. It does not restrict the receiving state from declaring a diplomatic agent, wherever located, as persona non grata.
Issuing a notification to the head of mission is not the same as physically entering the premises.
Article 22 has nothing to say on the matter of declaring a diplomatic mission member persona non grata. Article 22 is about the premises of the mission, not about the status of mission members.
Article 9 says
The receiving State may at any time and without having to explain its decision, notify the sending State that the head of the mission or any member of the diplomatic staff of the mission is persona non grata or that any other member of the staff of the mission is not acceptable. In any such case, the sending State shall, as appropriate, either recall the person concerned or terminate his functions with the mission.
The process of declaring a diplomat persona non grata changes that diplomat's status to no longer having diplomatic agent status and associated immunity in a receiving state regardless of where the diplomat happens to be currently located.
Note that the process is irrelevant for non-diplomats "hiding" in an embassy.
Diplomatic immunity applies to "diplomatic agents" not to visitors and not to "the administrative and technical staff and of the service staff of the mission". The former can be declared persona non grata, the latter not acceptable. There is a distinction.