I'm pretty technical, but even looking at the March 2023 Security Bulletin, I don't really know what I'd be looking for to determine if there's anything in there that might have caused a conflict with Messages/RCS and AdAway.
If there's a changelog for Messages Beta releases, I'm not aware of it.
Strangely, when I woke up today and several times throughout the day, AdAway 6.0.1 running VPN mode with the latest Messages Beta installed started having the same issue. I couldn't send or receive RCS messages. Had to disable the AdAway app to get anything through.
I unenrolled from Beta for the stable version. Currently have messages.android_20230220_00_RC03.phone_dynamic installed. With the same 6.0.1 VPN version, I'm have the same issue. This version was released on March 7, so that predates the release of the March 2023 Pixel update.
Any other ideas?