Point a domain you already own at Bottled and you get hello@yourdomain.com in about a minute. Mail arrives in the Gmail you already read, and replies go out from the branded address, so there is no second inbox to check.
Auto-reply handles the ones that land at two in the morning. Everyone who writes to you becomes a contact with tags and stages. Hand support@ to a teammate without sharing a password. Your own app can send through it with an API key.
Free tier, no card.