I just posted about the same issue but on Mac. Looks like when you paste a link into Asana it is automatically prefixed with https:// and sometimes the app link is removed (ie notion:// or craft://).
Since the system then sees https instead of the app link it directs to a web browser instead of the app.
Incase it’s helpful, you might find your link has been converted to something like https://craft://myCraftDocumentLink. If so you may find it works if (albeit via a web browser) you alter it to look like https://myCraftDocumentLink. This works for notion links but will be app dependent.
Hoping they can adjust this soon so DeepLinks work as expected!
This is the ticket I added for reference if it is useful to anyone: