Is wearing a belt absolutely necessary for barbell medicine programs?

I know there is science behind the benefit of wearing one, but I just don’t like the idea of buying or wearing it. Is it more of a recommendation or do you consider it super important?

On some weeks of the bridge, Monday squat is with belt and Friday is beltless, can these both be done beltless as long as following the set/rep/ and RPE correctly?

Sure, go for it.