Just to clarify your point, that’s correct for PA, but it is not the same in every state. Most states allow the governor to replace the senator until a special election can be held but some have restrictions on who the governor can appoint, some require the appointee to be from the same party as the outgoing senator and some require the state house to approve the appointee. 4 states do not allow the governor to replace the senator at all and require a special election.

https://www.pewresearch.org/fact-tank/2022/05/03/how-do-states-fill-vacancies-in-the-u-s-senate-it-depends-on-the-state/