M/C is the common abbreviation for "machine".
I don't know what you mean by Edge notifications for gmail.
Do you mean click the three dots in the top right, go to "settings", "cookies & site permissions", then "Notifications"? If I turn "Ask before sending" to "off," I get the same tone plus half the proper sound. Allow still has gmail there. If I change the "allow" gmail to block I get no sound and no flag.
When I did that, the sound and flag stopped on my Win 10 laptop too. I checked the settings on that and there was no gmail there, I put the same as on this computer and the sound is back again.
The way I try it out is to send myself an email from another email address. After doing the above, on this computer I got the proper sound the first time. When I sent another, it was back to the tone and half the proper sound.