Look for low budget options: Renovation obligations? New construction?

Forget quickly about the standard land value as a benchmark for price determination. Somewhere in the deepest Eifel in a small village that might still help and plots of land are actually sold for that, but not here. I live in your first mentioned desired region and the closer you get to Luxembourg, the more expensive it becomes. Actually, this is relatively structurally weak country but Luxembourg massively drives prices up, the economy is currently doing very well there and the employees from the border region can choose their jobs and pull the local wage level considerably upward, which then is reflected in the actual paid land or house costs for an actually very rural area. Of course, these are not big city prices here, but bargains near Lux you will only find if you really consider unconventional properties (so off the beaten path, isolated location but not suitable for horses or the like) and then renting them out will probably be difficult if no infrastructure is available.

Mobile home on the campsite and then rent a garage nearby?

I had that idea too ... when I click on campsites that would suit me perfectly in terms of location, however, I read "The campsite remains closed over the winter months as usual, ..." Permanent campers: "Season 1.4. – 30.9." and at one where the permanent camping pitches can be used year-round, that a primary residence outside the campsite must be proven (which I would NOT have with this model, since the mobile home would then simultaneously be my residence?)

and the closer you get to Luxembourg, the more expensive it becomes.

if, then best with residence IN Luxembourg (due to cheaper tax regulations/health insurance contribution) whether in the mentioned areas 100 m or 100 km outside Luxembourg then doesn't matter ...

You don't have to live in Lux to have the tax advantages. You just have to work in Lux, then you also pay taxes and social security contributions there. Most Germans don't want to live in Lux at all. Especially not with children (see Lux school system). Significantly more Luxembourgers move across the border into Germany because they can still afford a house here. The Germans are just daily cross-border commuters (after Corona).

You only have to work in Luxembourg, then you also pay taxes and social security there.

wrong:
I have a few capital gains in my portfolio
these would be taxable in Germany upon sale, in Luxembourg (since the stocks have been in the portfolio for a long time) tax-free
and here the place of residence counts, not the place of work

besides, I have worked enough for the last 18 years - and regarding health insurance I think:

Voluntary health insurance
...
To benefit from the voluntary optional insurance, the applicant must:

[*]be resident in Luxembourg;
[*]...

...
The contributions have been 107.58 euros per month since January 1, 2014.

in Germany I come to AT LEAST 400 to 500 euros monthly

Most Germans don’t want to live in Luxembourg at all. Especially not with children (see Lux school system).

I have no children

the only annoying thing I have discovered so far is that I have to present my car(s) in Luxembourg every year for the "recurring technical inspection (main inspection)" instead of here in Germany every two years

Auctions are a bad example. Such a starting bid of €160,000 is ridiculously low. What would you have been willing to pay at most?

What do the common real estate portals show as interesting examples in your desired region?
Is there anything already?