Ellipses as pauses is a leftover of telegrams which bled into the era of limited text messages(and/or charging by the text), because the financial incentives for long single messages were the same.
In the era of unlimited texting, though, we’ve dropped that convention because it’s extra keystrokes. In fact, we’ve even dropped the period at the end of sentences in texts because you can just hit the send button as a thought separator, sending multiple texts.
Including the period is unnecessary extra information, so it is seen as formal at best or even a way to covey unhappiness, anger, or frustration.
Hope this helps! Note that none of this applies to longer form messages like this one.