You may not want to disable notifications for the Mail app entirely on your iPhone since you could miss essential emails when they come in. But you can at least silence conversation threads on an individual basis. Doing so won't mute all conversations from the same sender, only the thread you select. Plus, it works for group email threads where things can get chaotic.

Muting a conversation in Mail works for any thread, but you'll see the most benefit when muting a particularly chatty group email conversation where you'd typically get alert after alert after alert. Silencing threads will not move them anywhere in your Mail app — they'll remain in the inbox marked unread just like usual — you just won't get notifications from the Notification Center.

To start muting email conversations, you need to be running iOS 13. If you have other iOS devices running an older iOS version, they will not be muted. Same thing if you sync with iCloud to Mail on macOS — you need macOS 10.15 or higher. However, if all of your devices are up to date, the silenced thread will be muted across your iCloud account, meaning no notifications on any devices.

There are two ways to mute an email conversation thread in iOS 13 — a swipe gesture from any folder's list, and a tap from within the email thread itself.