Maybe low birth rates put the whole world into stagflation. Maybe they don't. Maybe low birth rates lead to a return of imperialism and mass war. It's in the uncertain future.
I disagree. I actually think there is more than enough data to argue that prosperous societies are not the end state of capitalism. The are the middle state of capitalism and the end state is increasing market power abuse caused by the proliferation of oligopolies and monopolies, which leads to stagnation on multiple fronts and societal decline. This makes sense when you realize the core tenet of capitalism is severe restriction on what the group can tell an individual they can and can't do with their capital, labor on with their labor or think about with their intellect. When the system is functioning properly it's basically a self regulating society improving idea machine because if you come up with an idea that people like you sell it in the market and amass more capital, which amplifies the reach of your ideas and labor. That process just keeps repeating as long as you output good ideas. When you output bad ideas that nobody wants you fail to sell it and you lose money on the sunk costs, decreasing the reach of your future ideas.
This amplification has a negative downside in that as you increase one's reach you increase their ability to block other's reach and thus you naturally get monopolies/oligopolies. For a capitalist society to continue to stay in the awesome middle stage it needs government to both mostly stay out of the way and also come in and break up monopolies/oligopolies and government seem to pretty uniformly fail about both of these tasks.
side note: it's unusual in history for low birth rates to lead to a return to imperialism and mass war because war is usually expansionary and needs high birth rates to motivate both the need for expansion and deteriorating conditions at home to drive the support of said expansion. The only example of low birth rates causing expansionary war I can think of is the current ukraine thing and that is really more about decreasing border exposure for russia because their population is shrinking so fast they soon wont' be able to field a force that can defend the multithousand km plains border they would have with NATO if NATO held Ukraine.
Russia has long had a colonial ethno-state element - the vast territory predisposes a federal model, but the best way to secure control over many generations is through blood ties to Moscow. So what's enacted through the war - what makes it a good scapegoat - is a vigorous restatement of the status quo: at least, as planned, they were going to take Kiev in a few days, call "mission accomplished" , and resettle ethnic Russians in the region. The emphasis on civilian targets is a "you aren't valuable, your land is valuable" kind of statement, inherited from the Soviet period, and from the monarchy before that.