Send email on trigger action does not work.

Should I install sendmail to be able to send emails via trigger to all my agents?

It looks like you didn’t understand the difference in between a Zammad email channel and a notification channel.

The notification channel is not used for trigger emails at all, the group the ticket is in (and thus the trigger fires in) decides on the outgoing email address.

You can learn more about triggers here:
https://admin-docs.zammad.org/en/latest/manage/trigger.html

Unfortunately you’re permanently mixing agent notifications and triggers in this thread so it’s not exactly clear what the real problem is.