If there are people out there who are well invested into Gmail, then here's an alternative (https://klinger.io/post/71640845938/dont-drown-in-email-how-...) that does not require a separate client application. The initial concept is focused on desktop usage, but with a small modification it can be adapted to mobile-based working as well.
For years I've used Gmail Filters to apply labels to specific "from" addresses. Takes a bit to set up as I have very long "from(@domain.com OR @domain2.com OR ...)" queries but ideally I'm also unsubscribing from newsletters etc. that I don't want.
I also use multiple inboxes as well. First, "Starred" (different colored stars means different things to me and this strategy is used consistently across multiple platforms inc macOS labels, Trello etc.), then "Alerts" (critical emails from various systems), then "Important and Unread", then everything else.
Most emails are not "important" and I do actively unsubscribe so the method is manageable for me. The last thing I need is my email inbox to be a giant todo list. Most important are tech/work related, current projects, finance/business. I try not to sign up for anything that I need to read, newsletters etc. That's what RSS is for. Email is for quick actionable item and some communication.
I star a handful of emails max. each day. Not laborious at all considering the work load offloaded to Gmail's filters and I use a red, orange, yellow, & green star system.
You can already do an inbox-zero-like workflow in slack.
In Prefereneces -> Sidebar set slack to only show "Unreads and starred conversations". This reduces the list of channels to these two things. (Edit: it might be a good idea to star all conversations that need followup, first).
Muted channels (which I make use of a lot) will still not trigger notifications, but now you'll know that, if it appears in the sidebar, there are unreads there.
I star any conversations that comes up and needs followups or actions. When I'm done with it, I unstar it and it goes away.
This has worked wonders for me and I highly suggest the same workflow to everyone.
Note that after the latest Slack update, it should be possible to make use of the groups feature and use them together with the workflow above. This way you can have multiple statuses like TODO, awaiting reply and delegated, like in the parent article, rather than a single set of starred conversations. So far I haven't felt the need for this personally.
Oh and one more thing. In Preferences -> messages and media set it to "Compact", it will declutter the UI a bit.
Hiding the list of conversations doesn't medan you have to keep away from them. You can still jump to windows and write to people using the search bars and commands! :-)
When I was at Google, Tim Sneath taught this same workflow to the whole team. It was the only way to handle the Google scale email firehose. Now that I'm in an Outlook shop, been looking for a way to replicate it.
The instructions are mostly up-to-date, main thing that has changed seems to be that the multiple inboxes option is now under Settings->Inbox->Inbox type->Multiple Inboxes
I've been using it for years but I can't figure out how to make it work on mobile. Gmail mobile (web and app) simply doesn't have those various icons for stars.