The online requirements for Postman (and now Insomnia) was a deal-breaker wether to use it at work. We opted for Bruno[1], which is local-only
I'm not in love with the fact that it advertises itself as open source, but when you dig into it, there's a fair number of features that apparently belong to a source proprietary payware fork.
(Not affiliated with them, but am a user. It's not as featureful as Postman, but often good enough.)