Non- resident business banking is effectively already gone since 2019 - some banks are more protective then others so while ENBD did close already Rakbank,
Dubai Islamic Bank etc. keep banking the ones with non EU owner or EU owner that already got onboarded with a non EU address from for example
Thailand - back in the days.
When you look in the Middle East - taking all the cons in terms of ease of setting things up compared to the UAE - you endup in looking into
Bahrain - 10%VAT with no other taxes - banking like 10 years ago in the UAE.
Kuwait is very complicated to get things done and technically you need to involve locals.
So Bahrain it is but still if you won't make it with a bit of substance in Dubai dont expect to make it in Bahrain - everything is much smaller and less streamlined then in the UAE - talking about business setup and banking. For sure you can achieve what you are looking for but for sure not with the motivation "I don't want to get substance in Dubai that's why I'm now going to Bahrain" you will fail.
We have several clients especially with multiple passports living in Dubai getting themselves Bahrain Company under other passport for diversification purpose - however everyone is amazed how good things working out in the UAE compared to Bahrain.