In case anyone was wondering, Senate vacancies in Kentucky are filled by the governor from a list of three choices provided by the party of the resigning/dead/whatever senator's party. The replacement holds the seat until the next general house election, but this would coincide with the 2026 election for this seat anyway.
If he is resigning from the Senate all together the November timing would put Beshear in an awkward spot if he wants to run for the seat in 2026 since he'd be campaigning against whoever he appointed (which doesn't matter to any reasonable person, but the rubes would eat up that line).
Beshear has also gone on the record saying he thinks Kentucky's senator replacement law is unconstitutional, so this could also end up in court.