Hm, it’s close: 10^10 is 2^33.2, while a s16e6 number with exponent biased by 31 can represent 1.999 * 2^32.
So you either need to increase the bias by one or use a wider exponent. But I guess the intention was to allow s16e7, i.e. 24 bit floating point. 23 bit numbers seem quite odd.