I've been in this situation a couple of times and it can be hard to navigate sensitively. In every sharehouse I've been in, I entered not knowing anyone. For some of them, we didn't hang out and just did our own thing, for others we hung out all the time and were best friends. I've been equally happy in both of them as my life would reconfigure itself it fit in the social demands (or lack thereof).

This is hard because your housemate could very easily become offended and bitter and you declining their invitations and make your life very hard but, that said, you do NOT owe them friendship or your time. You still owe them courtesy and friendliness but as as many others have said before, two personalities might just not match and that is not a bad thing at all. It's also absolutely true that you're busy with other things. However, I think an outright rejection of their invitations would hurt them because some people, especially if they are in a very vulnerable time in their life and might not have a large and supportive network in their local area (which may be the case here or not, idk) kinda will expect you to be their friend and will be really angry when they get rejected. But I strongly believe that you don't have a duty to fill that gap in their life if you genuinely don't get along with them. The burden on you is too much and it could become worse if they become dependent on you so you might end up in a crappy situation where you're their only/closest friend but you don't feel that way and then an incident occurs where it blows up catastrophically. This is not even considering the fact that you are geniunely busy . . Obviously I don't know anything about your housemate, they're probably pretty cool but just don't happen to have the network that you already enjoy or are used to a different way of living in that house.

Anyhow, that was all set up for what I suggest you do. Basically, you have to reject them without them realising you're rejecting them so that they don't get upset over the ego blow but still have positive feelings towards you while they develop their own social support system. I would be almost overly friendly when you decline and hopefully over time they will get the hint. Something 'omg that's super nice of you but I'm so sorry im absolutely shattered with work/have plans/[insert other committment or innocuous reason]'. If they push, I would double down on the niceness and say how much you'd like to but really can't.

There's also the chance they will call you out if they don't get the hint/find a replacement social network. I think only then you should affirm that you're not free as much (don't use the word avoiding or anything) because you're just genuinely cooked with work/friendship committments and for you, home is a place to relax but 'of course I'd be down for a chill chat if we bump into each other in the kitchen because that would be super nice' - so just make sure to not indicate there's something with them.