In Settings and privacy > Notifications, each type of alert can be received on your device and in the notifications inbox, only inside the app, or turned off.
There are options for chat messages, comments, replies, mentions, supports, recognitions, new followers, posts from people you follow, consistency and draft reminders, professional reviews, achievements and Help My Mind announcements.
Under Community notifications, configure each community separately. For specific conversations, use Mute notifications in chat.