Does FindMinimum Work With Parametric Region Constraints?

Questions
1

In[40]:= FindMinimum[{x + y,
Element[{x, y},
ParametricRegion[{Cos[[Theta]],
Sin[[Theta]]}, {{[Theta], 0, 2 [Pi]}}]]}, {{x, -.7}, {y, -.7}}]

Out[40]= {1., {x -> 1., y -> 2.22537*10^-8}}

In[39]:= NMinimize[{x + y, 
  Element[{x, y}, 
   ParametricRegion[{Cos[\[Theta]], 
     Sin[\[Theta]]}, {{\[Theta], 0, 2 \[Pi]}}]]}, {x, y}]

Out[39]= {-1.41421, {x -> -0.707107, y -> -0.707107}}

The FindMinimum result is wrong, even though the starting point is quite close to the actual minimum.