How do random number generators in calculators work?
According to the manual, the random number is generated from a seed, and a new seed is generated after a random number is generated. Also the random number seed is user selectable to control sequences of random numbers.
All this gives information that it is a simple deterministic pseudo-random number generator (PRNG), something like a linear congruent generator (LCG), or a linear feedback shift register (LFSR).
Given the fact that this random generation must be repeatable, it makes sense to simply use pseudo-random generation instead of other kinds of randomness, even if it is tempting to use entropy from some sources like battery voltage level, timestamps of button press and release events, etc.
It seems that someone has (almost) figured the algorithm for the exact same calculator and has a webpage about it on github to calculate next numbers given the seed value.
Looking at the code, it's an LCG which uses numbers 40014 and 2147483563, of which the latter is a prime. These numbers seem to be quite popular due to a paper by L'Ecuyer on implementing LCGs, as discussed on United-TI Archives.