Try with fresh Kernel ?
$Version
(*"13.2.0 for Microsoft Windows (64-bit) (November 18, 2022)"*)
Remove["`*"];ClearAll["`*"];
Solve[m g Sin[\[Theta]] == m v^2/r && 0 <= \[Theta] <= \[Pi], \[Theta], Reals]
(*{{\[Theta] -> ConditionalExpression[\[Pi] - ArcSin[v^2/(g r)], Or[
And[
Inequality[-(g r)^Rational[1, 2], LessEqual, v,
LessEqual, (g r)^Rational[1, 2]], g > 0, r > 0],
And[
Inequality[-(g r)^Rational[1, 2], LessEqual, v,
LessEqual, (g r)^Rational[1, 2]], g < 0,
r < 0]]]}, {\[Theta] ->
ConditionalExpression[ArcSin[v^2/(g r)], Or[
And[
Inequality[-(g r)^Rational[1, 2], LessEqual, v,
LessEqual, (g r)^Rational[1, 2]], g > 0, r > 0],
And[
Inequality[-(g r)^Rational[1, 2], LessEqual, v,
LessEqual, (g r)^Rational[1, 2]], g < 0, r < 0]]]}}*)