She desperately wanted to avoid "bad scenes" at German borders.

IDK if the book of journalist Robin Alexander "Die Getriebenen" (the driven ones, meaning top German politicians driven by events) was ever translated to English, but that guy had daily access to the Chancellory and describes the situation to a T.

Merkel built her career on media appeasement and an illusion that Germany is in such good hands that nothing untoward can happen to it. It sort-of worked until 2015, when the outside world could not be kept at bay anymore.

I think she actually did, that and her Christian beliefs. Not all of politics is cynical, sometimes politicians are selfish and unreasonable and act on their principles. There were more fiscally prudent ways for Germany to increase its population for various political and economic ends if Merkel so chose to use them.

Not out of goodness of heart, but out of ideological conviction and obligation to international refugee conventions

Even if the will to have younger blood to fuel the economy is a driver for such a move, it has nothing to do with propping up pensions: in an aging population you'll need people working in your country if you want to keep things running, no matter how your pensions are being paid…

It's not because a politician say something that it's true, you should know better ;).

The reason why governments promote immigration is because they want to increase the workforce (and in the case of Portugal, replace all the emigrants from Portugal). As the population is aging, if you want to keep cheap labor you need new arms to work, no matter who pays for the pensions.