I'm in the same boat as the parent: ALL my clients use Slack, and none of them wanted to use Asana, so I gave up.

Sure, Asana does task management... but that's about all it does. Slack is a lot more casual, and you can create channels for each project and have conversations there about who will be doing which task.

Internally, we actually use Trello for task management. Honestly, it's far superior to Asana in terms of ease of use and flexibility. It has less features, but that just encourages keeping things organized in simple ways, which is great.