The question which still remains answered in such a context is: if a sub-group rejects what the main group perceives as their main contribution to the general culture as a stereotype - do they still hold ownership and copyright over it and to what an extent?
What has been perceived as gypsy culture - and especially their music - had a significant influence on central European artistic and especially musical developments in the 19th century.
If the Romani in the US reject that as a misconception - do they have any "copyright" over it?
Do those musician in New York even know or have to know that there is a connection between the gypsies of "The Gypsy Baron" operetta (one of the most important works of a very important composer of what we call today "classical music") and today's Romani in the US?
That question may remain, but once again, I'm afraid I'm not the one to help you answer it, because I don't care. I care about the ethics of cultural artifacts which may be offensive to peoples who have been traditionally persecuted. And I care about some aspects of copyright that I find troubling. But in terms of the specific questions you raise, I have no strong opinions, so I have nothing particular to say. Sorry.
As for stereotypes of Roma peoples in my country - as I've already admitted, I know far less about the specifics of their groups here than you do about those communities in your own country. I think the stereotypes here are broadly the same as the stereotypes in Europe mentioned so far in this thread.
I'm perfectly aware that all groups have positive and negative stereotypes that others apply to them. US Americans certainly have plenty of stereotypes applied to us by members of other countries. And within the US, we have stereotypes about Northerners, and about white, middle-class suburbanites. That's the way of the world.
But when it comes to groups that 1) are particularly vulnerable, and 2) have a history of being badly persecuted, even the "positive" stereotypes can be deeply harmful. Again, I don't know enough about Roma peoples specifically, but of the top of my head I could list "positive" stereotypes of Jews, Black people, Indigenous people, and some kinds of queer people and disabled people that members of those communities broadly agree are damaging.
(It's also worth noting that, in the US, at least, it's historically and even currently quite possible for members of majority groups to live their whole lives without ever forming a close association with any members of the marginalized groups I've just named; and so they have less opportunity to learn the truths and untruths of these stereotypes. Perhaps in Poland it's different with respect to the nomadic peoples we've been discussing, I don't know.)
I don't think, though, that the primary objection Roma peoples in my country have to the "g" word is its connection to the stereotypes. If I made that claim earlier, I was in error, and I retract it. I think they object because they view the "g" word as intricately intertwined with their history of persecution by majority groups, much as the "n" word is inextricably tied to anti-Black racism. And similar slurs which I won't type here which apply to other stigmatized groups such as other races, gay men, trans people, people with certain kinds of mental illness, etc..
I hope I've made it clear by now that I'm only talking about my country - which is also Corey's. From your testimony, it seems as though your communities in Poland have, as a whole, largely embraced the "g" word. And that's fine. There's a rich history of groups embracing names for them that started life as insults. "Gay" and "queer" are obvious examples. I understand "Tory" in England, has a similar history to it. Heck, my own religious community, a small Protestant offshoot calling itself the Religious Society of Friends, was disparagingly nicknamed Quakers early on - and faced a fair bit of persecution in their first several decades - and that's the name we most commonly use to refer to ourselves.
However, it's a very different matter when a community, as a whole, rejects a word for or image of itself that's been applied to it from outside, and this goes twentyfold when the community in question is a minority that has centuries of history of being brutally persecuted by the majority. We can see this in my country with certain Indigenous groups demanding that we stop using terms that were slapped onto them by others, as opposed to their own words for themselves. And more power to them.
(Heck, even without the history of persecution, I don't see the harm, here. If a critical mass of Germans demanded we all switch to calling them Deutchlanders instead, I'd have no objections to that.)
Again, I understand from your posts that the situation is very different in your country because the communities in question in have not collectively rejected the "g" word. I also understand that, in my country, they absolutely have, and so I will follow their leading on this matter when in my country, and/or addressing an audience primarily of my countrypeople. I will, of course, change my language as appropriate when addressing people of other societies where the consensus about what is and isn't considered a hateful slur are different.