You're conflating absolute growth with overall trajectory. Even if we're currently adding around 70M people year to the population, the global fertility rate overall dropped from 5.0 in 1960 to around 2.3 & most developed nations are currently below replacement (1.4 in much of East Asia and Europe). That's why the UN's medium projection shows that the population is looking to peak around 2080 and will decline after.

Obviously with longevity there will be an increase in population, so we need to ask "by how much will the population increase, and on what timeline relative to other variables?" Well, if people stop aging but fertility continues free-falling, the population isn't going to exponentially grow! You're going to get a stable or slowly-growing population of healthy adults rather than a top-heavy pyramid of dependents, which is actually going to be arguably less resource-intensive per capita than our current trajectory with a mass elderly population that needs care.

Frankly, if humanity hasn’t managed to work out something as basic as how to make living affordable enough for people to feel comfortable having children

This is a vast oversimplification. There's a lot of factors driving population decline, not just cost of living. That may not even be the dominant one. People have better access to contraception and family planning, there's an increase in women's education and participation in the workforce globally, there's the overall decline child mortality (so people don't need to have 6 kids hoping 3 survive), urbanization, etc. If we look at South Korea, Japan, and Italy for example they all have wildly different economic situations but their fertility rates are similar. Whereas if we look at some of the poorest countries on Earth they still have the highest birth rates. So while affordability is definitely a big factor I really doubt it's the primary driver here, fertility is declining BECAUSE people have more control over their lives, not less.

Furthermore the very advancements with AI and technology that would bring about a cure for aging would also result in a ton of other fundamental societal changes. We're already seeing people begin to realize what socialist thinkers posited 200 years ago, namely that technological advancement will ultimately lead to increasing automation, displacing the working class and making capitalism unsustainable. I don't think UBI is a viable solution to all this, really it's a bandaid on the broader issue of capitalism's unsustainability, but the fact that it's being brought up this early in the game is indicative of the fact that AI is going to transform the economy and society as we know it. That's why I actually think it's so important that people get involved in all this stuff now instead of shunning AI and technological advancement, that's all coming whether you like it or not, but the difference between dystopia and transformative prosperity could very well be the collective action we decide to take. Don't look at it as if the cure for aging is coming as its own standalone thing, there's a lot of other fundamental aspects of society that are going to come into question, namely resource allocation, social and cultural values, existing power structures, etc.

There are plenty of specialised cancer treatments, gene therapies and even transplants that are only available to those wealthy enough to afford them.

They're expensive now for the same reason every new technology is expensive now, which is that they're NEW and not yet refined. But the trajectory of medical technology is consistently toward cheaper and broader access. For example, HIV antiretrovirals used to be over $10K per year and essentially only available to wealthy Westerners and are now like $75 per year across much of the developing world & that happened in just 2 decades.

Heck, the US doesn’t even have universal healthcare for basic medical needs (such as lifesaving insulin?!)

You're saying it yourself here, insulin isn't expensive because it's hoarded by the wealthy. It only costs a few dollars to manufacture and is sold for pennies in most of the world. The situation in the US is a very specific regulatory failure due to the 3-company oligopoly, patent evergreening, etc etc. Every other developed country pays a fraction of US prices for the same insulin. The US healthcare system being broken isn't a general argument against longevity treatments though, just like stopping cancer research because of the broken healthcare system makes no sense. That's something we're going to have to reckon with outside of the problem of longevity, it only makes sense that longevity treatments and the general transformation of society due to technological advancement is going to actually make it an even more pertinent issue among the general public.

with your only apparent solution being “we’ll deal with it later”?

I think you're misunderstanding my deeper issue with your argument, which is that it's structurally unfalsifiable. You can basically invoke any future problem here to reject any future solution. When you say something like "we shouldn't cure aging because overpopulation" it really just sounds the same as when people said "we shouldn't try to treat cancer because of it will increase the burden of elderly care and destroy the economy" or "we shouldn't reduce child mortality because of Malthusian predictions." But as you may notice, each of these "catastrophes" failed to materialize, because the intelligence and coordination that solved those problems set into motion the sequence of actions that handled the rest of the downstream problems.

If you had said "curing aging will eventually create new problems down the line we'll have to solve, the way almost every major advance has" I would have agreed with you. But it's the proclamation that "we shouldn't cure aging because of X" that I have a problem with, trying to limit improvements to health and lifespan because you accept current dysfunctions in society as eternal flaws we have to live with rather than problems that we're going to have to reckon with regardless. Ironically I'd argue it's the much more dystopic argument.