Construction costs are currently skyrocketing

Yes, you just have to optimize that then.
You're right, back to topic.

Only where living is much cheaper, are well-paid jobs usually not available, or they are rarer. And also jobs that can be done entirely from home are not available to everyone, or are often blocked by old-fashioned bosses. If I were allowed to work 100% from home and could also do so from a family perspective (patchwork), I might not even live in Germany.

But what good is the better-paid job if the extra salary is eaten up by more expensive living costs!? I have been through that game: my wife and I decided for good reason to move our residence from Hamburg to Saxony-Anhalt. Both of us earn slightly less here than we would have in Hamburg. But rents here in SA were 5-7 €/sqm, the roll from the local baker 0.55 €, and a piece of cake 1.40-1.90 €. I was in Hamburg again over Easter: 2.95 € for a piece of strawberry cake. And real estate anyway! My personal opinion: better a detached house in Saxony-Anhalt for 300,000 € than a mid-terrace house in Hamburg for 600,000 €. For the monthly costs saved, I’d rather fly to Italy more often per year, go to a restaurant twice a week, or buy the 4th or 5th Rolex (as an investment). I am aware that this is not feasible for everyone. But sometimes you have to turn priorities upside down or reorient yourself when the conditions deteriorate. Not everyone here supports the AfD, and we don’t live behind the moon here either.

But what good is the better paid job if the higher salary is eaten up by the more expensive cost of living!?

A higher pension in old age, if you then move to a cheaper area (for example, somewhat outside a metropolitan area).

Both of us earn slightly less here than we would have earned in Hamburg

In my opinion, this is (still) the exception. As an example, I only have real sample data for Northern Saxony, where you earn only about 50% of what is possible in Berlin for comparable jobs. And Berlin is already paid worse nationwide. This will change, no question. At the moment, I am counting on having to be there in person only 2-4 times a month in 6-10 years, and then for me it will be off to the Lusatian Lake District or something like that. Unfortunately, it will not be much cheaper until then.

I'm at
you earn less, but part of the living costs is lower. I'll never forget how I once stood at the village bakery and the poor saleswoman had to recalculate three times because the cake couldn't possibly be included at that price. My sister pays 45 cents more for a butter croissant.
100 sqm apartment or single-family house larger than 100 sqm with garden, double garage for the same money.

A higher pension in old age if you then move to a cheaper area (for example, somewhat outside a metropolis).

Most (here) build in such a way that they are dragged out of the house by the undertaker. The little that I lack from the state pension, I build up myself from my surpluses.