Is financing a new single-family house feasible?

In the public sector, that can be accurate. I am employed in the public sector myself. As an employee in the higher groups, the difference between level 1 and 6 can be over €25,000 gross annually. However, that takes 15 years. It is quite illogical that someone gets significantly more just because they have been there longer or are older. This mostly has nothing to do with performance. These automatic step increases can be taken into account if they make a big difference. Although I think it should at least work somewhere with the current salary. Of course, you can earn considerably more elsewhere if you are good. But that always comes with risk and stress. A better, more responsible job is usually also associated with more working hours and pressure. You always have to weigh that up. What do I want and what has to be? Do I want more free time or do I sacrifice myself completely for the company? A good working atmosphere, security, and flexible working hours, especially with a child, are also important. Coming home only in the evening every day and having more money in your pocket would personally not be for me.

It is already far from any logic that just because someone is older or has been around longer, they get significantly more. This has mostly nothing to do with performance.

You have to compare the public sector with really large companies. There are very similar automatisms in the collective agreements. In general, the very large German companies are very similar to the public sector.
Another example: external service providers automatically cost more with longer professional experience (Junior/Senior). They also don’t have to take an aptitude test beforehand. Of course, in daily work they then have to prove their experience... but even that is not a performance test situation.

These automatic step increases can be taken into account if they make up a lot. Although I think it should also work at least somewhat with the current salary.

Hmm... the discussion is drifting too much towards my case now. First and foremost, I factored in my master's degree with the switch to the hD.
But even without it, it would have all worked out. Of course, more narrowly.
But for medium- to long-term planning, one should definitely forecast their salary development.

Yes, that's true that other companies also have so-called "Erfahrungsstufen". However, 15 years is exaggerated and is also one of the reasons for the shortage of skilled workers in the public sector. This also makes one not competitive with other companies. Although you can also negotiate the level. I still hold the view that just because someone has been there for 15 years doesn't mean they have more experience or expertise. It rather depends on how much knowledge one has gained during that time. If someone has been doing the same thing for 15 years, they have rather remained stagnant.

Honestly, I don't understand your point. Do you now find the experience levels to be too generous a "gift" or a non-competitive "gift"? Of course, automatisms have the disadvantage of not considering individual cases. But in the end, it's about retaining or attracting skilled workers. And basically, an employee with many years of professional experience is simply more valuable than a newcomer. That's also how salary negotiations usually go after the interview. An engineer with 15 years of professional experience will always demand a higher salary than an engineer with 3 years.

The experience levels simply take too long in terms of time. Whether someone has been in the same position for 5 years or 15 years makes no difference at least in my field. I already had more expertise than the rest of the department just one year after completing my training. For various individual cases, the public service offers hardly any great opportunities to skip levels. And even with a promotion to a higher pay grade, one could lose their time progression if this happens shortly before the step increase. Whoever came up with that.

I find these step increases totally luxurious. My girlfriend has been getting "just like that" a little over 500 EUR gross more per month since January. But that was the biggest jump in her pay grade. Now four years of waiting and then there will be 150 EUR (or so) more. But in between there are still the collective wage increases.

From what I have gathered so far, life in the public sector is definitely sustainable. As a commercial employee, one can only dream of that ;) In the next life, I’ll also go for the public sector :)