Your first step toward making Messages less annoying should be to the number of alerts you receive. Go to Settings > Messages > Notifications. Here, you can choose if you want to be pinged immediately when you get a text, or if you’re okay with receiving alerts as a part of iOS 15’s Scheduled Summary (this feature sends alerts only at preset times of the day). If you choose Scheduled Summary, be sure to keep Time-Sensitive Notifications enabled to ensure that you do not miss important alerts.
Next, if you have a lot of unread messages, you can get rid of the red notification badge that appears above the Messages app icon. Go to Settings > Messages > Notifications and disable Badges under the Alerts section.
You can also go to Settings > Messages > Notifications > Customize Notifications and change a few more useful settings: Under Allow Notifications, select which categories of notifications you want alerts for. This lets you disable notifications from Unknown Senders, or message categories such as Transactions or Promotions. Mute notifications for the messages you don’t need to see right away.
You can also tap Repeat Alerts on the same page and set it to Never to stop Messages from pinging you twice for every incoming message.
If you are a part of too-chatty group texts, you can mute conversations to stop notification spam from disturbing you. Open the Messages app, swipe left on any chat thread, and tap the purple crossed-out bell icon to disable alerts from that chat only.