This is great. I suppose the improvements will arrive soon. I used to use Thunderbird on Android long ago. (K-9 has done it's part in filling the gap sincce then.)
It has always been a neat system to use - Thunderbird on desktops, and on cell phones(used to be on iphones also, I think.) though not linked, the same freedom of self mail control. A very good way to archive all your mail, as you want, without externalities. IMAP and PoP.