An Ngram helps illustrate how British English primarily uses have got and American English more recently uses have gotten more:
However, in that long history, have got appears so frequently that I would be wary of calling it an error or a restricted usage. Obviously have got happens sometimes. Why?
Stroppy Editor explains the most likely reason - whether someone is talking about a static (possessing) or dynamic (receiving) situation:
In both countries, the past tense of get is got. In British English, the past participle is also got. But in American English, it’s more complex. Roughly: when talking about a static situation (possessing or needing) the past participle is got; when talking about a dynamic situation (acquiring or becoming) the past participle is gotten. So:
Yesterday I got a new guitar
I’ve got a great guitar
I’ve gotten a new guitar
There are a few more examples and more explanation, but I want to highlight the last two examples listed here. Notice how either got or gotten functions fine. According to the rough explanation, got suggests possessing a guitar; gotten suggests acquiring a new guitar. If we apply the same expectation:
I haven't got a response yet. (roughly static - they don't possess a response yet.)
I haven't gotten a response yet. (roughly dynamic - they have not received a response yet.)
This split in usage is affirmed by other sources as well (PBS, "Language Myth 21: Americans are Ruining English").