"Stamp" vs "stomp": when, how, and why?

In Britain, the two words stomp and stamp are used rather differently.

A stamp is a stamp, irrespective of whether it is done angrily or in excitement. I stamp on a twig to break it, or to flatten a piece of earth when gardening. Those do not involve anger, excitement, or a response to musical rythm.

But to stomp out of the room (in anger), or stomp to the music, or allow the children to stomp all over the house (when playing/enjoying themselves) is something different.

Personally, (and I am British), I would never stomp my feet merely to get the mud off my boots after working in the garden. That would always involve stamping. And a horse would never stomp unless it was a pantomime horse on stage, dancing to music. Horses stamp. And my sense is that stomp is used much less in Britain than in America. Most people in the UK stamp their feet in anger.

I find it difficult to conceive of a single stomp. If there was only one of them, for me it would always be a stamp. But to stomp means there must be multiple stamps.

The first recorded reference to stomp that the OED has is from 1845, and it is in a poem by Robert Browning, in order to obtain a rhyme:

1845 R. Browning Englishman in Italy 272

And then will the flaxen-wigged Image Be carried in pomp
Thro' the plain, while in gallant procession The priests mean to stomp.

I am British, in my 60s and I don’t remember ever hearing the word stomp in my youth. What brought me to look up its usage was repeatedly coming across the phrases ‘old stomping ground’ and ‘chomping at the bit’ in the media, including the BBC. I am sure it used to be ‘stamping ground’ and ‘champing at the bit’.