Voters living in a long-term care facility can find helpful information in the Fact Sheet for Voters in Long-Term Care Facilities, issued by the PA Department of State in August 2022.
Specific information pertaining to the need for a designated agent. From page 2:
An individual may serve as a designated agent for only one voter unless the relevant voters live in the same household. A “household” for the purpose of designating an agent does not include a long-term care facility. This means that each resident in a LTCF [Long term Care Facility] who is unable to return their own voted ballot due to a disability must designate a different agent. However, a couple sharing a room or apartment within a facility may be considered members of the same household. (emphasis added)
Read the entire PA DOS Fact Sheet for Voters in Long-Term Care Facilities