how about support ansi-color for the output of stdout/stderr in *Messages* buffer
I am not entirely sure what you are asking, as I am under the understanding that dape already supports ANSI colors, if that is set in comint-output-filter-functions.
Can you share the result of M-x describe-variable comint-output-filter-function? I belive that the default value of comint-output-filter-function changed in some quite recent Emacs version.
another question when I remove dape-repl from dape-on-start-hooks the stdout/stderr is in Messages buffer ,it does not supports ANSI colors,
The message buffer does not support displaying strings with text-properties