Purchase or construction in Berlin / surrounding areas, realistic?

Not necessarily, as developers can definitely work remotely. It depends on the employer. We have people who worked from Mexico or Thailand last year. So unless you have to plug network cables into switches...

For exercise, he can then use the stationary bike at home [HO]

An expert in the industry in Berlin also typically earns from 80 K EUR upwards (not only at corporations).
As said, IT entry-level professionals can easily demand 40 K EUR in Berlin. And with 3 years of experience, you are no longer a beginner.
The degree is also less important here than in other professions – you don’t need a degree, you just have to be capable.
One thing must also be said, Berlin has only been catching up for the last approximately 5 years, what was missing in previous decades due to lack of economic upswing. So, compared to other major cities, Berlin is still quite behind.

Please just cite the statistics from which you derive your data.

Those I can find state about 40k gross starting salary p.a. on average for a graduate computer scientist.

Besides that, it doesn’t really matter, the man must/can decide for himself where he works and for what salary. Of course, the demands regarding the property do not match the salary, I believe we don’t need to discuss that here. Absolutely unrealistic to want to build near a big city/metropolis with such an income. That only works with a lot of support (--> cash) from the family.

There is a well-known service provider for salary comparisons. There you can enter key data for yourself and receive a salary analysis with statistics based on regional reference. I simply entered the key data. Job profile Software Developer and for the degree, only vocational training was entered. The median was 55 TEUR but that includes all professional experiences and company sizes, which is why I went 10% below the lower quartile limit and ended up at 40 TEUR. Admittedly, this is not a cleaned-up statistic, but a good sample with regional reference and always very current, while public surveys are often very general and unfortunately based on old data. The other part is my personal sample in the circle of acquaintances, which makes my somewhat rough estimated number appear plausible. Which statistic did you find?

In Panketal there is currently a semi-detached house for sale for 400k. 102 sqm, built in 1997, rather small plot. If you want to use it as an interim property, that would be something. Scout-ID: 130623864

Unfortunately, you can't really say what all would need to be done there. I would rather go through it with an expert.

There is currently a semi-detached house for sale in Panketal for 400k. 102 sqm, built in 1997, rather small plot. If you want to use it as an interim property, that would be something. Scout-ID: 130623864

A single-family house is being offered in a popular location in Panketal. The residential area is characterized by new, modernized single-family houses, semi-detached houses, and terraced houses on leasehold land.
This suggests that this house is also on leasehold land and that in addition to the house price, there would be an entry into a heritable building right contract.

Unfortunately, you just can't say what all would need to be done there.

I expect to have to do little to the substance, with district heating you also do not have to replace your own boiler, but of course this coin has two sides.

I actually overlooked the issue with the leased land. Although I am personally against leases, I consider it more of a solution in this case. With the low salaries, unfortunately, you don’t stand a chance in Berlin. You could lease the plot of land and build a small house on it. Of course, you would then pay the lease amount and the land would not belong to you, but you would still have a bit more freedom than in a rented apartment. And since you don’t want to have children, there would be no heirs to leave the house + land to. If you don’t want to change either the salary situation or the location, that would be another option.