My ex (31m) wished me (29f) a happy birthday earlier this month, and now I feel pressured to do the same for him tomorrow. What should I do?

I KNOW, the simple answer is “just don’t text him,” but here’s the reason I’m over-analyzing the crap outta this…

We broke up early June after 2 years that included an engagement (ugh, shoulda said no). Unfortunately, I moved an hour away from my hometown for him back in December, and although he’s now living with his parents nearby, we still share rent at an apartment since our lease isn’t up until September (at which point all is in order for me to relocate back to my hometown). We agreed for me to live in the apartment until lease end since it’s full of my living things (plants/geckos), but he said he’d continue to pay his share of rent and leave his stuff in the spare bedroom. And I need him to help pay the rent – he makes more than double my income and has oodles of cash/taxable investments to spare.

At first, I was devastated when the separation happened, but now I’m so relieved it’s over. More than anything, I struggle with anger and embarrassment that I stuck with him as long as I did. Ideally, I would remove him from life completely. I am not one of those people who struggles to suddenly and totally shut someone out of their life, regardless of how intimate the relationship was. I am very aware it’s the best way for me to heal – stop caring or worrying about what they’re doing, allow myself to hurt and be sad/mad, and then focus on me, period. UNFORTUNATELY, I am unable to do so because I still have to communicate with my ex to pay bills and deal with all his s&@t still sitting in the spare bedroom as he figures out his next living situation. Which keeps changing. -.- I digress.

So, I’ve been very polite, short, and strictly transactional with him when we’ve spoken because that’s all this needs to be. He, conversely, has texted me “casually” a few times (I shut that down pretty soon after he tried it by replying, politely, in ways that don’t facilitate a convo), and when it’s a transactional convo, he always gives more details than are needed (which I never acknowledge in my reply). Like, frankly, I don’t care what his “exciting” future career and living situation opportunities might be even if it sorta relates to the convo at hand – it doesn’t concern me any more, so please don’t share those details. It feels dismissive of my attempt to move on. As glad as I am to be out of the relationship, I can still hurt over it.

…so yeah, this is a month after we break up – he texts me “Happy birthday!” first thing in the beeping morning on my birthday. I respond with “Thank you”. Convo over, thank god. But I’m angry af because now I feel this immense pressure to have to wish him a happy birthday on his birthday, too! Am I interested in doing that? NO. We’re not together, and I don’t/can’t care about him like that any more. But we share rent, and idk, he’s already retracted helping me pay to move back to my hometown – I think – because I haven’t given him a single dash of emotional attention since the breakup. So what do I do? Politely fake it with an 8pm oops-almost-forgot text for the sake of a few thousand? Or be true to the boundaries I set for myself and offer nothing but radio silence?

TL/DR: Ex can’t set conversational boundaries, but I feel obligated to acknowledge/respond to him because we’re riding out an apartment lease together and I need his financial aid to afford it. He texted me happy birthday earlier this month, but I don’t want want to return the greeting because I’m trying very hard to move on from a devastating separation. Should I *potentially* risk his help with rent by choosing not to text him, or should I fake it til I make it and wish him a “Happy birthday” and move on?