The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.
OP could’ve just repeated “spells do what they say they do.” It doesn’t say you lose control of your character in the new form, all it says about the new form and how that affects the character is…well, that line(plus a few other things about the gear they were wearing and whatnot).
But nothing explicitly states that you stop playing as the character you were playing as if they were transformed, whether into a playable character option or not. There is no rule saying that that character is playable, but there is no rule saying you can’t play as them. Again, spells do what they say they do.