I too have stepped in it before with a friend. Not the same blowback by any means as you are getting but an honest apology offered is all you can do.

A friend and I were casually making fun of eachother and telling jokes, he told a yo momma joke. I told a yo momma joke.

It was then he hit me with "my mom's dead, that's not funny" and I doubled down with "well dig her up and she'll be boned and rolled, I'll have her spinning in her grave". It turns out, he was not kidding when he admitted his mother had passed away(something we had never discussed prior).

I met him with "c'mon dude don't push BS" to make it worse. Next day I offered an apology and a day after we were right as rain, with a new topic to avoid. Though I should also note, he escalated with facts to make me feel bad initially, then genuinely felt bad he'd done that too, so there was a pair of us in it, both apologizing for diff reasons.

Since you have already sent a text apology and been left on read, silent treatment sitting beside them, time is all you can give it. If it's not sorted in a few days, ask to meet to offer your apology again in person (it's an opportunity to discuss) but if after that it's radio silence you can't continue to followup, chasing someone with multiple messages over and over just comes across as harassment.