Now this problem is resolved. In my docs (in ~\.bashrc ) there was a weird .bashrc that sets $PS1 to a new value using colors with the tput command. It does not exist in Git Bash and should not be there.
After commenting on the line where the parameter $PS1 was set / exported, everything became normal again.
The line was something like
export PS1="$(tput ...
(I do not remember him correctly.)
I donโt know where it came from, maybe I accidentally copied it there for cygwin ...
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