The creation options were rendered as a keyed list, so a field shared by
two games (target_score) kept the previous game's widget when the game
changed: after switching scopone -> briscola the input still showed 11
with scopone's min/max instead of the briscola default 61 (1/100 instead
of 61/120), even though the submitted payload was already correct.
Recreate the option inputs on every game switch instead, so each one is
initialized from the new game's defaults and schema constraints.