How does it differ from a volitional form without っと?
My best guess is that it's a monologue marker, like な is.
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Yes it's a sentence-ending particle which is usually used in monologues. One article says the main function of this っと is to casually convince/confirm something to the speaker themselves. Perhaps it's like saying 'okay' to yourself.
- 今日も1日お疲れさまでしたっと。 (before going to bed, to oneself)
Occasionally it's used when there's an actual listener. When that happens, it expresses the speaker's sarcasm or indifference to the matter or the listener.
- 俺はもう知らないっと。 I don't care any more.
- 「彼女ができたんだ。」「そりゃよかったねっと。」 (indifferently)