thanks for your answer!
Sorry for not providing sufficient background, I'll do my best to answer all the open questions:
Q1: Could you explain which tool and/or process along with PC
I'm on Windows 10, I used the Flasher tool from the WebIDE (Settings > Flasher).
Q2: Which version is being flashed and by chance do you recall what version was there, ballpark okay? One of these perhaps, or some other file?
The current version is 1v91, the tool tried to flash 2v10 for the revision 1.3 of the pico board (https://www.espruino.com/binaries/espruino_2v10_pico_1r3.bin)
Q3: Was any attempt made to try the 'Advanced Reflashing' ?
I did not. I read about this but I assumed that the device is (as of now) not broken.
Q4: Was an attempt made to flash directly from the WebIDE?
Yes, I only used the WebIDE.
I believe the issue is not the flashing tool or the firmware version to be flashed. It has probably something to do with the fact that after entering bootloader mode both LEDs are lit brightly and it is not possible to connect to the board any longer.
Therefore also the Flasher tool is not able to connect to the board and do some actual flashing.
The board so far works fine!
I can just connect normally and store some sample code and execute it.