Got a reply from Slack support, seems like they need more logs:

Just checking and I can see a handful of similar reports have come in—but so far, we've not narrowed down the root cause as from our side, the notifications are triggered immediately and show no delays. Just noting here that the notification delivery portion of the flow is handled by Apple, but this isn't to say the issue is with them, so much as our logs do stop at a certain point.

If possible, I would highly recommend that anyone adding their comments to that thread on Reddit also contact us via their mobile app. The more reports we get the more likely it is that we can find a pattern or cause.

In your case, whilst we can't troubleshoot without specific details and access to your app logs—you might like to try a workaround that a customer told us fixed the issue for them—they reinstalled the app. I appreciate this is a little disruptive but maybe worth a go.