In my personal experience, non gaming related, but shopping related is that customer service employees are just working off a script. So if you don’t resolve with them, it’s a dead-end in that regard.
Escalating by asking for a manager, these days to be considered a proper Karen move, is usually futile.
What may help in those regards is contact a higherup personally. Via these forums, consider a private message to reach out to either @Luxendra or @NW_Mugsy for example.
If that is to no avail, and it is still not clear on as to why you were banned, you can in this case also consider contacting Steam support, in case you have purchased the product via their platform. And explain to them that your product access has been suspended with no grounds provided.
That is of course, if no grounds have been provided. Up to you yourself to make the judgement call on that.
Beyond that, it’s just pretty much end of the line really. I mean, sure, theoretically you can seek legal council to act as an intermediate in discussing with AGS in this matter. But let’s be fair, who’s really going to do that for a 40 USD product.
Here you are already yourself providing a possible grounds for the suspension though, and it might already be coming to light that the ban was perhaps not as unwarranted as you have suggested it to be. And depending on whether or not similar crude language was also used in your engagement with customer support, this may have been the reason for a possible permaban.
Once more, I’ll leave this one up to your own judgement. You were there, we were not. But I would suggest you do question yourself on as to whether if crude language could have been grounds for a suspension, how was your interaction with the support staff? Was it a respectful conversation? Was it disrespectful or condescending?
Especially when approaching a third party, e.g. Steam support (if purchased via the Steam platform), your own interaction will obviously be of impact in any further outcome.
Highly doubt that would make any difference ;).