Asynchronous communication is largely a cultural concern, not a technical one, and completely compatible with Slack. Just give people permission to treat Slack as an async tool and remind them they don't need to be present there every minute of the day.
Where I work, we encourage people to close Slack when they need to focus or simply don't feel like being present. There's no expectation that a message gets an immediate response, even if the person is online.
While this is generally true, is how I recommend to treat Slack, and how I treat it myself, the reality is that its nature is neither here nor there.
It's true that if you treat it just right, you're going to get an async tool. However, you want tools that are naturally like that. There are many foods I can fairly easily cut with a spoon, yet my experience is much better using a knife.
The mere fact you have to encourage to close Slack means it is used for something it shouldn't. Use evergreen communication for most communication, then use Slack only when you need it, which will be much much less.
Slack is also terrible at history preservation, see my reply to a sibling comment.
History preservation is not just about continued existence, but also about discoverability. Other forms of communication (issues, project planners, and email lists) are much better for the latter.
I honestly don't even see the argument for why this is true of email lists. I went from an email-list-heavy environment to a slack-heavy environment, and both have been pretty equally good/bad for this.
I do think issues, project planners, design documents, etc. are better for discoverability, but they are also, in my experience, far less complete a history of what's been going on, than whatever the primary communications platform is.
There has been a lot of useful work that gets done in the cracks between the planning and work tracking artifacts, every place I have worked. I think you can either make that persistent and discoverable, despite it being super noisy, or just lose all the context on it altogether.
Asynchronous communication is largely a cultural concern, not a technical one, and completely compatible with Slack. Just give people permission to treat Slack as an async tool and remind them they don't need to be present there every minute of the day.
Where I work, we encourage people to close Slack when they need to focus or simply don't feel like being present. There's no expectation that a message gets an immediate response, even if the person is online.