If you look at list of confidence motions - all sorts exist. Some have focused on both govt confidence and PM. eg this from 1965 tabled by Heath:
— Dr Catherine Haddon (@cath_haddon) July 12, 2022
That this House has no confidence in Her Majesty’s
Government and deplores the Prime Minister’s conduct of the nation’s affairs. https://t.co/1ESonIsvJG