Bash snippet to log all output (stderr and stdout) to both the console and a log file without any other script changes needed.

in-script-output-logger.sh

   #!/bin/bash
   
   # Aby thing that is outputted to either stdout or stderr is then sent to _OUTPUT_LOG_FILE from that point on (along with going to console).
   # Problem - when the script ends, "tee" seems to wait for input before continuing.
   
   declare _OUTPUT_LOG_FILE="~/logoutput.txt"
   # use base4.1+ timestamping %([%F %T])T
    # shellcheck disable=SC2312
    if ! exec > >(while read -r line; do printf '%([%F %T])T %s\n' -1 "${line}" | tee -ap --output-error=exit "${_OUTPUT_LOG_FILE}"; done) 2>&1; then
        printf "Error %s encountered when trying to startup log file (no error available)\n" "$?"
        exit 1
    fi