I would say that any time it is muttar to talk during davening ie. before hodu (n. sefard) or boruch she’amar (ashkenaz) it is probably muttar to text as well.
The halachos that talking during davening are derived from would apply to texting as well.
The only question is what is considered a hefsek in general. If I wash for hamotzi and then go play a game without talking, do I have to wash again to eat bread?