We are trying to customize the following email
Subject: [Forums | Site] Your account has been silenced
You have been silenced from the forum until November 13, 2021, 6:01pm.
Reason - Test
Testing
We have found how to customize emails such as the one found in below:
/admin/customize/email_templates/system_messages.silenced_by_staff
However, this isn’t the same as the one we received. Any tips on how to customize the specific one we received?
Thanks in advance!
Bumping this for recognition.
I’m not 100% sure this is working as expected.
system_messages.silenced_by_staff is the template for the pm the user receives, and that would(/should) only be sent out as an email according to their email preferences (and system_messages.unsilenced is the same).
The email in your OP is from where you enter the reason in the Silenced screen:
Leaving the second box blank would suggest to me that the default template (system_messages.silenced_by_staff) would be sent instead, but actually it seems to send this email out separately from the pm template, and it only sends what you’ve put in the box:
(my test user received this short email, as well as the longer template pm - but then did not receive a follow up email regarding that pm).
I tried copying and pasting the template into the reason box as a workaround, but it did not like the parameter fields: (and the links look right, but go nowhere as they have parameters in the url)
I could not find a template to change for this email, but it seems like there’s some scope for variation, if that’s any help?
However, the ‘unsilenced’ one works as expected. A pm is generated from the system_messages.unsilenced template, and an email is sent as long as the user has the correct email preferences set up.
Email received by test user:
Sorry I couldn’t be more help, but I thought sharing my run-through might encourage more replies. 
I seeing the same thing with silenced users. I agree with @JammyDodger that this doesn’t seem to be the intended function of the ‘Email Message’ field since no default message is ever sent in the silenced_by_staff email.
FWIW I also found an earlier thread mentioning the same issue: Feature request: Add reason for silencing the user to system message template
