I already solved this problem; just writing it down because I couldn't find anyone else who had it.
I'm using T-Mobile (LTE, not 5G) in the US on a Fairphone 3, which is a European model of phone. (I'm not sure it's relevant; I'm including it because it might be.) At some point after I started using the service, I was entirely unable to send SMS messages, but could send MMS, so I could send group text messages and texts with attachments, just not one-on-one texts. (I could receive SMS messages just fine.) I worked around this problem by attaching an image that was a blank white rectangle, and explaining what I was doing, when not using alternate chat applications.
Then I poked through my settings for a bit and discovered that I had left VoLTE disabled (to fix a problem I can't remember the nature of anymore, except that I remember it working). I re-enabled it, and then the next time I tried to send an SMS message as a test, my messaging app (Signal) made a request to send the message, which I of course granted. It sent just fine after that.
I'm writing this down because a couple of searches I made while trying to troubleshoot the issue returned no useful results, and I want to keep that from happening to any other users if I can.
