Hello, Vinoscopy.
I understand the Accessibility feature Spoken Content isn’t working within the Messages app. I often use Siri to read my incoming texts and am glad to have a chance to help.
I would first like to ask if this behavior continues after forcing the Messages app to close and then reopening it. If it does, I would suggest restarting your iPhone as the next troubleshooting step.
How to force an app to close on your iPhone, iPad, or iPod touch
Restart your iPhone
If the issue is unresolved after performing these two steps, I would next ask you if Spoken Content works when being used in other apps on the iPhone. For instance, if you open a Safari tab, are you able to highlight text and then have it spoken back?
If you ask Siri to read back a text, will they? For instance, does "Hey, Siri. Read me back my last message." work?
Please take note of these answers as I would like to ask you to contact Apple Support if restarting the app and iPhone do not resolve the issue for you.
I hope this helps and I wish you all the best.
Best Regards.