The /e modifier can be dangerous because it runs the resulting string as code. It is basically an eval() wrapped inside a regex engine. Nonetheless, if you know the content of the file, the sed command is one of the shortest to replace unix timestamps in a file.
# default format used by date
$ sed -E 's/([0-9]{10})/echo ""$(date -d @\1)/e' test.txt
Fri Jan 22 14:00:31 2021 my log entry