It’s totally fine to use the maximum tyre pressure.
The only thing I’d worry about with high tyre pressures is if your rims are too narrow for the tyres you are using. Rim sidewalls can break when used with too wide tyres at higher pressure. It’s especially problematic if you have rim brakes and are wearing away the sidewall over time. But it looks like the Alpenchallenge has disc brakes and relatively wide rims, so no problem there.
I don’t think your puncture had anything to do with pressure. You could change to more puncture resistant tyres if it happens more often.
If you have punctures on opposing sides (called “snakebites”) and without any sharp object involvement it can be because of too low tyre pressure which causes you to “bottom out” and pinch the tube between tyre and rim (that’s why they are called pinch flats).
Your weight is indeed on the higher end for a “normal” bike. The thing which is most likely to break are spokes on the rear wheel. This is relatively harmless. A 32 spoke wheel won’t collapse with one or two broken spokes. But you should check your wheels regularly and look if they are still true (less than ±1mm side-to-side wobble of the rims). Try to go over bumps carefully. Lift your backside from the saddle and use your legs as shock absorbers.
The brakes could overheat on longer descents if you let them drag.
Edit: In my experience this tyre pressure calculator gives pretty good results: https://info.silca.cc/silca-professional-pressure-calculator For your 140kg system weight and 35mm tyre width it recommends a little over 4bar (60PSI), which is surprisingly low and I definitely wouldn’t go lower.