I had originally included the switch in the light group because the video instructions here included the switch within the group for Smart Switch with Smart Bulbs setup.
However, I had the thought to remove the switch and try binding it that way as you suggested, but the lights did not seem to respond to commands.
For additional info, the lights included in the group are the Juno wafer downlights discussed in this thread, which may not fully support binding like some other bulbs might. So they may be a source of my issues, if so.
I’ll test binding my switch to some of my Hue bulbs in a bit and see if the issue remains.