Device stuck in flash mode on RPI3 64b Bookworm

[jointerCZ]

Hello,
I have a strange issue.
I have RPI3 with 32b Bullseye, flashing Lililygo Supreme ESP32 via Chromium was fine.
Done it at least 5 times. The OS is maybe 8 years old, upgraded over time.

I moved the Lilygo Supreme to different location where I have the same RPI3 model (both are the 100Mbit LAN version) and installed 64b Bookworm on it.
When flashing, I can put it to flash mode via the 1200bd button, it flashes, but never exits the flashing mode.
Switching it off and on does not help.
The only way out was to connect it to Windows PC and flash it from there.
It gets stuck on line "Leaving" if I remember right, where the Windows PC was also displaying line like "hard reset via RTS pin."
Is there a way how to do the reset to normal mode somehow? Maybe adding a button in the web interface to switch back would help?
Or do I need to install something to do it via commandline? I was looking into how I can flash from commandline and it seems doable, but did not tried it yet.

Also, when I tried to use RPI3+ (1Gbit LAN version), I was not able to enter the flash mode via the 1200bd button at all. Tried several times and also OS reinstall.
Using the same SD card in the older RPI3, this reset started working, but then the devices does not exit it...

Can this be related to the 32/64b difference?
Unfortunately I cannot do more testing, as the device is hard to reach (roof).
The purpose of the Pi is to allow remote flashing, as it is not possible to flash via wifi, only via BT and only via iPhone app, which I do not have.