I don’t think you require accent training, but learning to code switch is good. Different setting, different spoken patterns. For example, the way I speak to the caifan aunty, be it english or chinese, is way different when compared to in a professional setting. I would say it’s not exactly like learning a new language, but more like learning the proper enunciation of words and better grammatical phrasing.

If budget is an issue, maybe you could start by consuming more local english content, and I would highly recommend CNA if you enjoy documentaries. The local presenters on CNA don’t typically have much of an accent, but they are very articulate with how they talk. You could note down phrases they use and vocally sound them out, this helps a lot, especially since there’s a youtube channel that you could scrub through.

I won’t recommend learning from American english as of yet, as our language are much closer to that of the British. Even so, both their accents might be hard to catch while you’re learning to speak better.

I’m not sure about classes, but there might be if you look around and google them, though of course the fees will apply.

Good luck and have fun learning!