Temporary redirection of stderr in a bash script

exec 2> /dev/null
progname >& ./tmp/run.txt && run_status='OK'
exec 2>1

exec 3> /dev/stderr 2> /dev/null
progname >& ./tmp/run.txt && run_status='OK'
exec 2>&3

exec 3>&2 2> /dev/null
progname >& ./tmp/run.txt && run_status='OK'
exec 2>&3

progname > ./tmp/run.txt 2>/dev/null && run_status='OK'

{
   progname > ./tmp/run.txt && run_status='OK'
} 2>/dev/null