First, we need to be clear that this is informal free punctuation used over social media, which explains why it is not well-documented. It is indeed an increasing tendency, as social media spreads more and more.
The book Kill Reply All, written in 2020 by Victoria Turk (features editor at WIRED UK), does make an attempt at analysing it:
Grammar traditionalists look away now, but you might even witness some people using the nascent "comma-ellipsis"—an ellipsis made of two or three commas instead of full stops. This is by no means widely used, and only ever in a very informal context,,,
The nuances of the comma ellipsis have not yet been codified, but a callout to my Twitter followers garnered several potential explanations, with some people suggesting that it indicates irony or is meant as a less "serious" version of the regular ellipsis, which to some people apparently looks a bit angry these days...
I have also found a well-written and serious article on the phenomenon, written by Thomas Moore Devlin in 2019, which does not advocate for the legitimacy of the comma ellipsis, but simply points out it exists and tries to understand what it conveys. It's a long article: Why Do Young People Use Commas So Weirdly?, so I will only quote key points:
The comma ellipsis is not caused by someone missing the period button and hitting the comma one instead. One answer on the Reddit question by user “hagearty” explains why people use the comma ellipsis instead of a period ellipsis sometimes:
aestethic and comedic value. they express a different voice over text.
“and i’m like,,,,”
“and i’m like…”
i read the first one as being more dramatic, more annoyed. the second expressed an ellipsis’ original function of trailing off. I use it mainly over text, but imo i use it because the people i text use it so, kinda up to the social aspect of language.
and yeah, sometimes it’s just kinda goofy. Brandon Wardell’s twitter is an example of that.
I have emphasised the words that describe the meaning attributed by this user to the comma-ellipsis. The author of the article continues:
As this answer implies, the comma ellipsis likely evolved as a direct response to the period ellipsis. As ...
became the formal option for pausing and trailing off, ,,,
became an alternative that allowed for a more emotional reading or, counterintuitively, a more comedic reading. Commas, just by not being periods, call more attention to themselves, which conveys to the reader that something else is going on. The comma ellipsis can say either
I’m trailing off because I’m upset!
or
I’m trailing off or pausing but also I’m joking!
Ideally, surrounding context clues will help you distinguish which one it is.
This article also gives instances where the regular ellipsis (...) can send a negative signal:
While older generations think this sounds fine, younger people tend to read ellipses as ominous. I, for example, had a boss who always ended emails with ellipses, and nothing sends shivers down my spine more than seeing an email end with “We should meet soon…”
A 2018 article in The Outline tried to tackle the root of the ellipsis phenomenon, and hit upon a basic generational divide. While millennials see warning signs implied by what’s omitted in the ellipsis, older generations see them as a neutral trailing off in speech. “See you around.” sounds to some people as too serious and finite, and so they opt for “See you around…” even though that sounds like a murder threat to other people.
The author concludes:
These text ellipses allow people to string informal, incomplete thoughts together without wrangling them into formal punctuation. They aren’t so much a trailing-off as a brief pause in a stream of consciousness. For a generation that has never used them in that way, their proliferation can easily be read as ominousness.
Just to end the discussion, here are some answers of Twitter users to the question: Also, what's up with,,,,,comma ellipses,,,,,,? asked by the Canadian linguist Gretchen McCulloch. They will convince you that Twitter users are more likely to use it than not:

Other answers say:
- only when texting..mom uses two periods..she’s a native Arabic speaker..
- i use them! it makes the sentence softer. also sort of fits with using incorrect/atypical punctuation as cutsey – e.g. i;m instead of i'm.
For more on the subject of new tendencies in informal texting, here are some pertinent articles: