So relieved to have confirmation from
@kjm2, after being misled by an A level textbook endorsed by the leading exam board, that what I believed to be ‘not ok’ is indeed ‘not ok’🤪
No, it's not OK. In this testing set-up with a pre-chosen significance level, 0.05 is the probability that H0 is rejected, given that H0 is true. Not the same as the probability that H0 is true, given that H0 is rejected. The conditioning (the 'given') is the wrong way round.