It looks as though the app will simply stop working as of 1 June.
Samsung introduced Bixby with the Galaxy S8 in 2017 and stopped including S-Voice on its phones, a service which at one time was simply a standalone app. It never took off despite being a main rival to Apple’s Siri and was more of a voice command launcher than a fully integrated assistant. It bit the dust as it was replaced by Bixby, which has itself been overshadowed by the superior Google Assistant that is also available on newer Samsung devices.
Samsung said that its Galaxy Watch and Galaxy Watch Active have software updates to Bixby (if users haven’t updated already) and that similar updates would be pushed to the older Sear S3 and Gear Sport watches after 1 June.