redirect all error output to a file, &» /tmp/whatever.log isn't support by sh, so use command below instead:

12  *  *  *  * /opt/homebrew/bin/brew update >> /tmp/brew.log 2>&1
20  */3  *  *  * /opt/homebrew/bin/rsync -a -O --delete /Users/dcai/Downloads /Volumes/JUPITER/backups/duck/ >> /tmp/backup.log 2>&1
30  */3  *  *  * /opt/homebrew/bin/rsync -a -O --delete /Users/dcai/Dropbox /Volumes/JUPITER/backups/duck/ >> /tmp/backup.log 2>&1
40  */3  *  *  * /opt/homebrew/bin/rsync -a -O --delete /Users/dcai/Music /Volumes/JUPITER/backups/duck/ >> /tmp/backup.log 2>&1
50  */3  *  *  * /opt/homebrew/bin/rsync -a -O --delete --exclude "node_modules" /Users/dcai/src /Volumes/JUPITER/backups/duck/ >> /tmp/backup.log 2>&1
01  */1  *  *  * /usr/bin/curl 'wttr.in/Sydney?format=%l:+%c+%f' > /tmp/weather.info

Adding -O / –omit-dir-times to avoid setting times on directories (which causes errors in ntfs)