I've never switched devices part way through composition (and don't have my phone on me to test ATM). Could depend on mail app or email service as well as OS.
I've not met an app that resizes the keyboard from its normal behaviour. I'm surprised that the keyboard app co-operates - may depend on the keyboard of course. I just set size preferences myself where the keyboard app allows, but then it is easy for me as I rarely use the tablet in portrait and never type on my phone in landscape (too wide and keyboard takes up too much space), so only have to optimise one orientation on each. l'm curious, but not sufficiently to install Blue mail to test (I looked at it a couple of years ago, decided it was quite opaque on privacy, never went further).
Personally a tablet is my least favourite device for typing though - too big for thumb typing but too small for real typing (10-finger touch typist). I'm actually using handwriting recognition to write this (Note 10.1, so have that option).