Gypsies usually try to pass for South Asians. It's a step up.
In Prague years ago there was a diaspora to Canada of Roma and the news channels would constantly show happy Roms with free stuff saying everybody thought they were from Pakistan. The channels were undoubtedly encouraging Gypsies to migrate until Canada started demanding visas, Britain put immigration officers to stem the tide too.
The Roma have a terrible reputation which to a large extent they earned. They have never been able to assimilate anywhere in Europe.
I think it goes back to the caste system in india very old roots of the problem then in europe they occupied the untouchable status too in europe back then there was a similar caste system peasants nobility clergy etc then combined with their dark skin and very distinct look from tribal indians etc
As a whole they never assimilated but as individuals families and subgroups they more or less assimilated to a degree culturally and genetically but they are very distinct tribal indians so its harder to assimilate especially in a time back then where it was not as liberal as now and open to outsiders
