So WatchOS 26.2 did not fix this. Before updating to 26.2, I contacted Apple Support and they acknowledged that this is a known issue and that I should expect a fix in a future software update.
They did give me a workaround that has given me back the ability use dictation, but it is a bit clunky. You need to set your region in the AppleWatch app on your iPhone as the United States even if you do not live there. Then make sure that the top language is "English (US)". For this to work, the top setting on the region page needs to be "Custom", not "Mirror My iPhone." After doing this, I could get dictation to work in apps like Messages, but only if I manually choose "English (US)" from the swipe-up menu on the keyboard. After doing that, the mic icon shows up as an option. If I go into another app or close the app, then I have to repeat this process. It works, but you have to go through these unnecessary steps.
I do not live in the US, and I do not know if setting the watch region to US will cause other problems. So far, no issues have arisen from that.
I hope an OS fix is coming soon.
