I've kept my phone on silent via the physical toggle switch for the last four years and it's been a real game changer. I'm still notified via vibrations but receive zero audible notifications. It seems very odd at first but I'd have it no other way at this point.
What about the low battery nags?
When will the huddled high-device-usage masses be free of 10 of these a day?
Settings > Sounds & Haptics > Sent Mail > None
I said "iMessage".
Have you tried it? I honestly wouldn’t put it past apple for that one setting to control both things even though you can’t tell by the name.