How can I redirect standard error with [error] head?

I understand how to output standard error to a log file in shell.

BACKUP_DIR="/home/backup/"
BACKUP_LOG="/home/backup.log"
echo "backup start" >>$BACKUP_LOG 2>&1
mkdir $BACKUP_DIR >>$BACKUP_LOG 2>&1

When mkdir command fails, i get the message: no such file or directory

Is there a way to change the error message to something like: [error] no such file or directory?

I want to prepend the text[error] to the front of the error message.

Here's something to try:

mkdir $BACKUP_DIR 2> >(sed $'s,.*,[error] &,'>>$BACKUP_LOG)

Adapted from: https://serverfault.com/a/502019/506625.

Tested using

BACKUP_DIR="a/b/c"
BACKUP_LOG="junk.log"

mkdir $BACKUP_DIR 2> >(sed $'s,.*,[error] &,'>>$BACKUP_LOG)

and junk.log shows

[error] mkdir: cannot create directory ‘a/b/c’: No such file or directory

Also works with command grouping (I'm probably not understanding comment though):

TESTFILE1="test1.txt" ; TESTFILE2="test2.txt" ;
echo "Test1" >$TESTFILE1

# make sure 2nd file doesn't exist and remove test log
rm -f $TESTFILE2 ; rm -f $BACKUP_LOG

# Command grouping ; 1st command OK ; 2nd command error
{ cat $TESTFILE1 ; cat $TESTFILE2 ; } 2> >(sed $'s,.*,[error] &,'>>$BACKUP_LOG);

and output

$ { cat $TESTFILE1 ; cat $TESTFILE2 ; } 2> >(sed $'s,.*,[error] &,'>>$BACKUP_LOG);
Test1

$ cat junk.log
[error] cat: test2.txt: No such file or directory

File redirection syntax in the shell is flexible, but perhaps a bit obscure. To add headers to both stdout and stderr streams, you can do things like:

{ { cmd | sed -e 's/^/[stdout] /' >&3; } 2>&1 | sed -e 's/^/[stderr] /' >&2; } 3>&1

That will add "[stdout] " to the beginning of each line of stdout, and "[stderr] " to the beginning of each line of stderr. To redirect to files, you need to make sure you do the redirections in the correct order. For example:

{ { cmd | sed -e 's/^/[stdout] /' >&3; } 2>&1 | sed -e 's/^/[stderr] /' >&2; } >"$BACKUP_OUT" 2>"$BACKUP_ERR" 3>&1

The easiest way to do multiple commands is probably to simply define them in a function named cmd and continue using exactly the same syntax as above. Of course, you can also add newlines and whitespace to make this more readable, or refactor with some functions. eg:

#!/bin/sh

BACKUP_DIR="$HOME/backup/"
BACKUP_OUT="$BACKUP_DIR/out"
BACKUP_ERR="$BACKUP_DIR/err"

cmd() {
        echo do one thing well
        echo do this poorly >&5
        echo three
}

{ {
        cmd \
        | sed -e 's/^/[stdout] /' >&3; } 2>&1 |
        sed -e 's/^/[stderr] /' >&2; } >"$BACKUP_OUT" 2>"$BACKUP_ERR" 3>&1

The new-fangled process substitution is certainly cleaner syntax, but will not work in many shells (eg, it is a "bashism").