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He also pointed at a serious demographic problem:

“It is impossible to overcome the most difficult demographic challenges that we are facing only with the help of money, social payments, and benefits.” Expanding on this point, he stressed the significance of traditional family values and drew parallels between contemporary families and those of earlier generations. Putin prompted reflection, saying, “Remember that in Russian families, many of our grandmothers and great-grandmothers had 7-8 children and even more. Let’s preserve these wonderful traditions and revive large families.”

You could address some of that demographic issue and concurrently make Russia more influential by making Russia a place that people would want to move to and then permitting them to do so.

But trying to forcibly take over entities that were in the old Russian Empire probably is counterproductive to that. Russia's a less-nice place to be than before this kicked off. Makes it harder to draw immigration.

You're also probably right that just providing a child-rearing benefit isn't going to get people to have seven or eight children. However, economic instability has been shown to discourage people from having kids. And this war isn't exactly improving economic stability for people in Russia.