not sure if you're trans yourself, but in case this helps: as a trans person, when someone gets my pronouns wrong, it's more important to me to know they aren't doing it maliciously, so catching it and correcting yourself or just showing any kind of awareness or quick apology helps clarify in the situation that you aren't trying to be malicious or denying my gender.
The intention matters more than the mistake is what I'm trying to say - the mistake itself is not a big deal when I'm visibly trans and I expect people to get it wrong, I just want to know if you're safe to be around or not, basically.
Though I should say, once I was less visibly trans and cis-passing, a mispronouning can be devastating to me. Since it's rare, when it does happen, it makes me think I've done something terribly wrong with my gender presentation or the way I am speaking - it feels dehumanizing and totally disturbing now.
But tbh, the mispronouning only happens now with people who knew me before I transitioned, and usually only when they have not spent much time around me since I transitioned. They mostly remember me as my pre-transition self. It's habituated for them to refer to me as he/him regardless of my presentation, and when they look at me they are used to seeing a man, so they don't see a woman but instead they notice all the markers of my maleness.
Meanwhile, cis strangers who have no history seeing me as a man don't know to look for male markers, and what they see is a woman so they never notice the discrepancies and they never get the pronouns wrong.
Not all trans people have the same experiences, though - some are more disturbed by mispronouning regardless, so it's important to understand the sensitivities or experiences of the individual. I just wanted to give you my perspective in case it helps.