After some days of research, allow me to report what I’ve found so far. TLDR: this is an area of unmet need that could probably be met with some effort, i.e., it’s an opportunity.
I haven’t found any free/libre/open-source Android tools. There’s a good FLOSS system for the desktop: https://github.com/abb128/LiveCaptions. I installed it and it appears to work very nicely. But it hasn’t been ported to Android. Computing power is a concern (because the first thing the app does is a performance test) so it might need to be optimized in some way.
In the proprietary world, it seems the predominant captioning system on Googled Android is Google’s. According to what I’ve read online, it’s among the best-performing systems. It’s built-in to Google’s Android and only needs to be turned on to be used in phone calls. Not surprisingly, there aren’t a lot of developers rushing to develop captioning phone apps when a respected participant’s is already installed. There are numerous apps that add captions to videos, or take notes from the audio of recordings. Thus, that small slice of Android that is de-Googled (i.e., us) is not served.
There seems to be something special about the phone app in Android. One app, CaptionCall, requires calls to be “forwarded” to the CaptionCall app.
Anyway, I installed every app I could find in the App Lounge that looked remotely applicable, and only one worked: Ava. This essentially captions whatever the microphone hears. But it doesn’t work directly with the phone app. I suppose one could start a call, send it to speaker phone, then go to Ava and watch the words flow by (yours and theirs). But this is a clumsy solution that could pose a challenge to people who are not that adept with their phone. Also, receiving a call could be uncomfortable: “Hold on while I turn on captioning!” (fiddle fiddle fiddle).
In short, I think currently there is no way to do first-class phone captioning on /e/OS. However, FLOSS software exists in the world (if it is efficient enough to run on a mobile device), and the phone app is itself FLOSS, so in principle there is a visible way forward to add general live captioning as well as captioned phone calls, if developers choose to pursue it.
I suggest that this is a task worthy of pursuing.