There’s no standard rule for how one should format text messages or IMs in screenplays.
As with all formatting advice, any way you handle it is okay as long as your intention is clear and you don’t confuse the reader.
One simple way to handle text communication is to treat it like dialogue, but indicate that it’s different.
Nakul reaches for his phone.
[Note: Text messages are in italics.]
It’s not stopping!
He picks up his pace, quickly thumbs a response.
Sit tight. OMW.
Ultimately, how these are handled will be up to the director, but if you want to suggest the messages be displayed on screen or read in voice over, you may choose to hint at that in the formatting.