Thanks to notify-send.sh I can now update the mail notification from Neomutt in Ubuntu notification center since it allows to replace an existing notification. This should be available in more recent versions of notify-send (Ubuntu ≥ 22.10).
set new_mail_command="notify-send.sh --replace-file=/tmp/muttnotification -a neomutt -u low -i neomutt 'New Email' '%n new messages, %u unread.' &"
Beforehand I tried notify-send.py which didn’t quite work.