This is miserable for everyone. Don't make Slack the center of your workflow. Don't let spontaneous Slack chats dictate your process.
The manager's job shouldn't be to scour Slack for information and then ping every person who might need to participate in or read each conversation. That just amplifies the noise. It's terrible to be deliberately ignoring Slack for 30 minutes to focus on work, only to have your manager ping you back into Slack to make sure you don't miss something.
Instead, the manager should be forcing important conversations to happen outside of spontaneous Slack conversations. If something important is decided in Slack, the decision needs to be recorded in the tracking ticket, Wiki, or other important location. If it changes anyone's active work, they should be interrupted. Otherwise, they can pick up the information from the single source of record (ticket, wiki, etc.) rather than being expected to follow every detail of Slack all day.
Small groups working on tasks together should have private PMs or channels to discuss implementation details, not giant Slack channels with 10s or 100s of members.
A good manager will avoid design by committee and will stay ahead of the spontaneous Slack firehose by arranging planning sessions and scheduled meetings where necessary.
Don't let the Slack chaos drive your workflow. Don't try to make managing Slack someone's job. Manage the workflow first, deliberately rather than reactively. If important conversations are happening spontaneously in Slack too often, that's a sign that you need to fix your workflow.