In the longer term this depresses GDP per capita as resources have to be diverted from productive industries like high-tech manufacturing into extremely unproductive industries like aged care. Again, Japan and many Western European countries provide good examples of this in practice. Finally, as the reality of the broader economic decline sets in, second order effects start to take hold like brain drain - as young workers see higher wages working in more productive economies, they decide to leave, worsening the population pyramid and depriving the government of precious tax revenue needed to pay for aged care. (Japan and many Western European countries are sadly, again, examples of this phenomenon).
The short term effects you're describing of nominal GDP rising and per capita GDP falling is only true when populations are growing through bad immigration policy, which is what we commonly see in the US for example. Growing population organically and sustainably, or through productive immigration that targets gaps in the country's labor force, should never have that effect as the new member of the population should eventually increase GDP by more than the average existing worker today.
At an individual rather than population level of course, having fewer or no children is easier, which is why people are doing it. But this describes a local optimum only, while the true optimum is population growth.
As a final point I think older workers are generally more productive as long as they’re able to use the tools they’ve developed skill with. With the advent of computers and information technology older generations were unable to map their skills to the new way of work. Society existed in the state they were used to for 10,000 years and suddenly instead of being masters as the elder had been, they were bumbling fools - made more tragic in that they were otherwise highly skilled at what they did with a lifetime of experience. This colors our perception of the aged because we are still in the middle of that transition. But do you think you and I will be limited by ability to use information technology? Mental decline doesn’t generally start until much later in life, and people are doing careers into their 70’s with success.
This is absolutely wrong. The "aging population" will be larger than the "younger population" in any situation in which there is sub-replacement fertility + stable (or increasing, obviously) life expectancy. It's just that the ratio may stabilize but it will be <1.
Right up until you overshoot your ecological carrying capacity and the whole society collapses, of course. That part tends to be less optimal.
I would note in my own life we waited a long time to have a kid because we wanted to be engaged in our careers early on. Once we had a kid we decided to stop simply because we enjoyed the focus on our daughter and didn’t see having a ton of kids as a social imperative. That puts our family at below replacement rate. My experience isn’t particularly unique among the parents I know, and we are actually younger than many.
I know all of the above is anecdotal and conjecture, but I’m fairly confident if I did my normal citation and data collection I would largely be supported (having seen the data and analysis in the past) but I’m sick and have too little energy right now.