“Sorry” is a phatic expression in several anglosphere cultures. You don’t say it because you’re sorry, you say it because that’s what you say when you… do anything. Sorry, would you like some breakfast? Here it is, sorry about that.

It drives her acutely nuts. I really try not to, and I frequently end up chewing my tongue while the word struggles to escape my lips like a mad cat in a bag, and then it slips out two minutes later anyway.

Over the years I've been able to reduce my sorries by 50% ~ 75% by making a conscious effort.

I've also taught myself how to stop signing off emails with "Thanks," when I'm not expressing gratitude.

I ended the ‘Thanks’ train also. My signature now just says ‘Regards, my name’. One for the other I suppose :)

'Regards' -> Normal Interaction, 'Kind Regards' -> You've done something to annoy me, 'Kindest Regards' -> You've really pissed me off!

I would love to get out of that habit as well. What are you signing your emails with in those cases? Just:

- Name

?

Exactly. Just dash and name, except where I've made a request that they might choose to not honor, in which case I do sign off with "Thanks,"

My family member's mother in law writes emails like:

"Dear X, I hope this letter finds you well... warmest regards"

She will never be convinced not to.

I'm partial to "Cheers"

I used Cheers for a few years but I found it’s sometimes awkward for North Americans.

They associate it with alcohol toasts more than a polite sign-off.

They understand it’s a polite sign-off conceptually, but in the back of my mind I wondered if it rubs North Americans the wrong way subconsciously.

Its definitely off-putting if what comes before it is in any way "douschey" or arrogant.

"It is your birthday."

From what I can tell, what you're describing is exactly my partner's experience: she really can't help it. Try as she might, it comes out anyway.

I should learn to better control how I react.

(As it happens, she is francophone, but I'm not sure it's relevant as we mostly talk to each other in English.)

It doesn’t really count as an apology if you deliberately mispronounce it.