When you review what you have for your Sleep mode's settings, does it also indicate that it will allow notifications from that app when the mode is active? I found modes to be a bit confusing with respect to DoNotDisturb since it almost seems to offer two different places where things like notifications can be set, in terms of what one might have set in DoNotDisturb settings and then separately what one might have set within the mode itself for when that mode is active. I think of DoNotDisturb as basically a specialty mode. And, I think it isn't hard to unintentionally set things that conflict with each other. Probably also why it seems they got rid of DoNotDisturb on some devices or for one of the beta versions (but I think that just annoyed and confused people further).
I deleted the default Sleep mode and don't use it because it screwed with my watch in a way I had no control over for changing the displays. Then, I created my own "Bedside" mode. In both DoNotDisturb and my Bedside mode, I have them set to only allow the exact same certain app notifications scenarios through (because for me that's what I wanted), and for me it all works. However, my DoNotDisturb is probably quite different than what most have. Mine basically silences all sounds from anything except certain apps for certain contacts, while still allowing the actual notifications to be displayed normally.