derech hamelech- “The halachos that talking during davening are derived from would apply to texting as well.” Says who? Just because texting during davening is certainly improper doesn’t give you the right to make up new halachos. When chazal didn’t allow one to talk, they didn’t say anything about writing or texting.
“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?” If you talk you don’t have to wash again, so why would you if you texted (especially according to you that it’s one and the same). Obviously if you were mesiach daas after washing you would have to wash again, but I don’t know what the texting aspect adds to the question of what is hesach hadaas.