How to find an object (house/apartment/land) nationwide in Germany?

Of course, it could look different just 10 km further. You should only feel comfortable within walking distance. Whether it’s the pretty chapel that invites you to dream or the weekly music rehearsal that drives you crazy, and that dialect you don’t understand.

Just google Bad Kissingen or Bad Bocklet
Many of your wishes could be fulfilled.

E.g. Immoscout 111839176. but there are others as well.

I already like it a lot in terms of the apartment itself. I haven't looked up the area yet...

Nice property, but 2,500 rent is quite steep for a 4-room apartment. You could afford it. There is enough equity to draw down.

I already like what concerns the apartment itself. I haven’t googled the surroundings yet...

The luxurious 4-room suite is located on the first floor.
The salon is really large, with around 44 m² a place where family and friends will gladly meet.
The balcony offers enough space to turn it into your open-air dining room in summer.
There are various new buildings standing close together there.

Sounds like a spot of total peace and quiet. If only neighbors didn’t move in who use their own apartment exactly as described in the exposé.
By the way, I see seclusion differently – not paved over with multi-family houses (even if high-quality). As compensation, there is no local supplier in the village.

Since I myself am car-free, my first thoughts go to places that are car-free themselves, e.g. some of the German islands (I am not afraid of cabin fever on an island).
But also a penthouse apartment or even just a quiet location would be suitable.

I would proceed differently. Choose one (or several) regions that you like in terms of landscape (this seems to be at the very top of your list).

On foot, that is hardly avoidable.
I have been car-free for 20 years (and that doesn’t just mean I don’t own one anymore, I also haven’t driven one since then), and especially since I don’t plan to go to relatives’ neighborhoods, we simply have to shop on foot. Yes, a bike would also work. For now. In the next few years...

I wouldn’t go to an island. It would also be important to me that hospitals etc. are nearby.

Of course there are quiet apartments within walking distance of shopping facilities. I can think of dozens of villages in beautiful landscapes that fit this description.

I agree with that peace and a central location do not really contradict each other, and I would proceed as suggested:
Islands would be off-limits for me since senior-friendliness also means being flexible enough to reach specialists by bus and train or even a hospital sometimes. It is what it is.
Flat country also has its advantages if you use a bike. Then it depends on whether you like water.

Since I now, for example, personally often take short trips within Germany with my husband, I know few places by lakes and coasts. Every time I say: look, here is a nice apartment close to the water, beautiful daily fitness in nature, and behind you is the small town. So far, almost everywhere has been nice. Living where others vacation would appeal to me. One place is windier, another has a harbor. One has the community by the water, the other a bit further inland. One is a spa town, the other has a thermal bath.
Everyone has their preferences: that rules out East Frisia and touches on Rügen. Does Rügen have a hospital? If not, then maybe the Müritz area. Oh, no inclination toward the East? Then maybe Grömitz? Too conventional? Then Travemünde might be something. Ebbs, flow, tides-person? Or rather the mountains or hills, a bit further south toward Italy...
But it’s no use me listing our experiences for you now: surely you have learned to know and love one or the other place. Just because an island is kept car-free doesn’t make it a preferred option. There, you are often the stranger, which is not nice either. Small communities have almost everything you need. As a pedestrian also safely.

Personally, I would only rent anymore. And that somewhat centrally in a place with a fitness center, doctors, nearby recreational area, and train connection to a big city. The town center must give me security. I have to feel comfortable when I step outside.
Why should I still bother with a garden if it doesn’t bring me anything? Why strain myself with a second rent in a condominium?
If you have the money, then go for it. For me, Malle, Andalusia, or Rhodes would also be options.

What hobbies do you have? Golfing, swimming, hiking, shopping? Handicrafts were not an option. Maybe reading, education, volunteer work? Think about where and how you can best realize yourself, and then look for the place.