For 敨, what semantic notions underlie 'rap, tap' with 'to open; to unravel; to breathe; to rest'?
I think you're overcomplicating this.

咅 = tǒu = provides the sound
攵 = general movement/action = provides the meaning.

The components of 敨 basically just tell you that it is that verb pronounced tǒu. Seeing that it is used widely in dialects it is even more likely that it is just borrowed for its sound (and meaning of general movement) and used to fit where ever it seems rational.
I have seen other variants of this character in Sichuanese, like: 㪗 and ⿰咅支. I'm not sure if there is an accepted standard set character as many resources disagree.