Hi Simon; Welcome to Permies!
Nice little building. I just love clay brick buildings!
My first thought is smooth it out , tamp it down well,and put down a portable rug to sit on.
Using linseed /
flax oil as Burl suggested would help to seal it.
Despite all the growth on the outside I think I would want a window opening to allow air flow. Is it not very hot humid there?
The last question is not related to your floor but I am wondering about reptile visitors? Seems a dark cool cave would make a fine napping place for possibly dangerous snakes?
This is just my own phobia, as in my area of norther Montana we do not even have rattle snakes , my mind automatically thinks King Cobra when I think Burma!
Good luck sealing your floor and enjoy your meditation house.