The issue is resolved for a few days now and I made sure the solution is solid.
First the powersupply is a original Raspberry Pi PSU, but as i t ran for like 4-5 years now 24/7 this could have been an issue for sure.
But it was not.
I tried testing the system with an other script, that just writes something into a log, same behavior. Script gets executed only when turning the player off, and then it executes twice.
The thing that resolved the issue was a setting on the LMS side, in Settings>Player Tab> Audio settings of the corrosponding player: I had to switch the Power On Resume settings from „Pause at power off/Resume at power on“ to „Stop at power off/Restart song at power on“.
With that change the behavior that was pre existent for years is back, the script gets executed for one time when the player is turned on and when it gets shut down.
Edit:
I want to add how I got to the solution. I accidently clicked the pause button in the iPeng iOS app befor actually shutting the player down, on my way to power off the amp by hand again i recognized that the script wasn’t excuded twice. I actually tested that for a few days. Always first kill the playback befor powering the player down and it worked.
Oh and also the player didn’t crash for like 5 days now. I guess that makes sense, as most of the time I listen to web radio, and maybe just pausing that for 12h will crack the players head open.