The client shouldn't receive a notification when you manually mark a quote as "Accepted," UNLESS they're included on your email CC or BCC list. That is because this treated as more of an "internal" action by default.
However, if you would like the client to be notified when a quote is manually marked as "Accepted" or "Declined," then you can add them in one of two places:
1. Add them to the CC or BCC list either on the template level in the Email page using {{contact.email}}. Then click Save.
2. Add them to the individual quote itself. You can type in plan text here. If you use {{contact.email}}, this should automatically convert into plain text. Click Update when you're done.