Going through all of your channels you don't need immediate updates from and doing /mute will go a long way to getting the silence you want. People can still @mention you to get your attention if needed. You can check muted channels on your own time when you feel like it. You should also set up Do not Disturb and turn off the red notification dots.

The rest is a cultural problem that exists will all communication channels (including email). Ask people to be mindful and not use @channel all of the time (you can disable @channel if it is abused). Ask people to keep their chats to relevant channels. e.g. Daily interesting links do not belong in #general, please keep it to #random. Stuff like that.

Also, encourage people to move long complicated topics to a thread (to not annoy everyone in the room). Or ask them to compose a larger email or wiki page on the topic.