after some analysis I finally found the issue now. I analyzed a few things: WiFi channel width, encryption, config, password with/without special chars etc.
Note: it is no problem if special chars in the PW are used and it seems it is also no need to escape them anymore!
I found in my WiFi router security settings WPA2 with SHA256 being set which caused the client RECALBOX failing to connect and appear shortly as LEGACY device and disappear afterwards. However, the option WPA2 without SHA256 was also set and I expected a connection fallback to this option which did not happen!
Therefore I opened an issue to the project on Gitlab, please find a more detailed description here: https://gitlab.com/recalbox/recalbox/-/issues/1492
The workaround now was to de-select the option WPA2 with SHA256, or create an additional VAP (virtual access point) for clients which do not support WPA2-SHA256.
Hopefully, this thread and information should help also other members which have troubles to connect. Looking forward for your feedback and a happy new year 2021!