Is domo arigato considered formal?
Context: Buying something at a store, thanking a waiter, etc
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ありがとう、どうもありがとう、ありがとうございます、どうもありがとうございます is polite in order of increasing. I think ありがとう、どうもありがとう is usually used in this context but it is better to use ありがとうございます and どうもありがとうございます for important person like your master.
It is considered somewhat formal, but you actually don't thank someone for their service to you. It's more or less a cultural thing, in which the person working is expected to perform their job with or without praise. As a result, it can be a little confusing when you thank someone in the service industry for doing their job. It's not like you telling them that makes too big a difference in their lives, nor does it truly motivate them to keep doing the job they're already being compensated for. The paycheck is their thanks, not your saying so. The only times in which you would use some variation of "arigatou" is when someone OUTSIDE the service industry performs a task for you or if you receive a favor or a gift from another party. For example, I thank people on HiNative for providing me with clear answers or detailed explanations of words or sentences I cannot make sense of on my own. There are likely other cases, but these are the few that come to mind at the moment.