This is the second phase of Putin taking control of Wagner. Their response will very likely be to follow his orders so they don’t join Prigozhin.
Follow Putin’s order to not join Prigozhin isn’t very smart, but most people aren’t.
Prigozhin shouldn’t have held his breath wondering when Vlad would strike, but he definitely should have flapped his arms after it happened.
I don’t expect them to do literally anything. Wagner is now dispersed across Belarus, Russia and Africa; those in Belarus and Russia don’t have their heavy equipment anymore (taken away after the coup). Their leadership is decapitated, the two most important people in the PMC are dead along with several other higher-ups. The coup from 2 months ago wasn’t endorsed by the whole PMC, it’s been estimated that Prigo had only around 8k people with him - so today you should expect even fewer to rebel.
The “best” they might be able to achieve is some terrorism. But they’re not trained for terrorism, so for them it’s probably best to keep their heads low.