Google's Messages app says text message sent by SMS Pixel 4a, Android 11
As in the title, why does Google's Messages
app says sent by SMS? (Text messages are sent by SMS anyway, why emphasize?).
See below OK in the screenshot.


This is a self answered question, to share a new feature. Also, to answer questions that may be asked about this in the future (mark them duplicates).
Today morning, I got a prompt asking me if I wanted to enable chat features on messages app. I did that and saw the info on the SMS sent yesterday. Dug, to know more, and here's the summary from the Google FAQ on chat features :

You need the messages app as default SMS app.

Chat features are support is region/country/carrier specific.



When using chat features, your messages are sent using the Rich Communication Services (RCS) protocol over Wi-Fi and mobile data.





Show you when someone is typing
Offer read receipts (show when someone has read or received your message, as well as showing your contact when you read their message)
Send messages over mobile data and Wi-Fi
Lets you share files and high-resolution photos



Sending over Wi-Fi doesn't cost, over mobile data will be as per mobile data plan.


To answer the question, recipient doesn't have this feature enabled on their app and therefore SMS was not sent over Wi-Fi or mobile data and sent as normal SMS. It is only highlighting this aspect. Similarly, if you were to send MMS content in the same situation (feature not enabled, data not used), it would show as

If chat feature is enabled and sent by data, it would show mobile or Wi-Fi as the case may be.