Using Ubuntu 24.04.2.
The first time a newly created webapp launches, it shows up correctly in the dash icons; that is, it has the icon I assigned to it, the name I assigned to it, and I can right-click it to pin it to the dash.
All subsequent times I try and launch it (even by clicking on the icon I had pinned from the first launch), it does not show up as an instance of the correct assigned icon, it shows up as a duplicate of the Webapp Manager icon in the lower part of the dash, with a name like "chrome-messages.google.com__web_conversations-Default" or "chrome-app.ynab.com__-Default", and when right-clicked does not have a pin-to-dash menu option available.