How would you react?

[StreamingCervix]

If your partner said in a drunken conversation ‘oh shut up, I’m bored of you now.’ In a nasty, dismissive tone.

he seems to think I’m being silly and overreacting today, but has apologised. I feel like he leans towards being a nasty drunk, and don’t want this to be the rest of my life.

Ask him not to drink then. I don't think that comment is particularly a problem if he is lovely the rest of the time. As a pattern, not so good.

It is disrespectful, I'd give him a mouthful back but move on once hes apologised. I'm sure there will be chimes of 'emotional abuse' and 'ltb' soon though 🙄that would be an overreaction in my book for a one off. However if it became a regular thing that would be different.

If this is a regular occurrence then get rid of him.

A one off? A warning not for it to happen again and stick to it.

I wouldn't want to be around him when he's drunk, and if he insists on inflicting his problem drinking on others then I'd have to conclude that his apologies are worthless.

It’s probably happenIng about once a month, averaged out.

I feel like being spoken to like shit is eroding the love I do have for him over time.

Well my dh says stop going on sometimes (tbf I do analyse a situation a lot if I’m anxious).
He said it to me this morning and I told him I could voice my opinion if I wanted however he didn’t have to listen.
However if he told me to shut up because he was bored of me I would tell him not to speak to me like that.
The second time I would tell him that drunks are the most boring people on earth so he needs to check himself first.

My DH was a bit nasty to me once after drinking wine, I told him the next day and he apologised profusely and now refuses to drink wine in case it happens again. It's the response that's important here OP, saying you're silly and overreacting is a big red flag because it means he prioritises him being able to do what he likes over your feelings so he minimises the effect his behaviour has on you.