Direction of forces acting on points A, B and C

In this equilibrium position we can split the weight G in 2 weights of G/2 which we can attach elsewhere in the rectangle AB, in locations symmetric w.r.t. the middle of the rectangle ; for example, one in A and one in B.

Then the weight G/2 in A simply pulls downward in the point A, and the weight G/2 in B can be considered as if it was attached to A and C by strings or rigid rods with no weight.

Then the weight in B pulls on A and on C with forces F_AB and F_CB as for example explained in https://socratic.org/questions/a-particle-of-mass-10kg-is-suspended-by-two-strings-that-make-an-angle-of-30-and, or any other page you can find by googling "mass suspended on two strings".

So, for your question of the direction of the forces in A, B, C: In C we have only the force F_CB in direction CB ; in B we have the weight G/2 pulling downwards, compensated by the opposite of the forces F_AB and F_CB, and in A we have the force F_AB in direction AB, plus the force G/2 downwards:

So, to know the direction of the resulting force, we have to compute F_AB.

To this end, let's call φ = arctan( L /(L/2)) = arctan 2 ≈ 63.4° the angle of AB w.r.t. the vertical, as for ⍺ in BC.

Then we have the equations
(1) (sin φ) F_AB = (sin ⍺) F_CB
(2) (cos φ) F_AB + (cos ⍺) F_CB = G/2

Maybe the easiest way to solve this is to add (cos ⍺)(eq.1) + (sin ⍺)(eq.2):
Then F_CB cancels out and you have (cos ⍺ sin φ + sin ⍺ cos φ) F_AB = (sin ⍺) G/2 = G/4.
Also, if D = sqrt(L² + (L/2)²) = L √5/2 is the diagonal AB, then sin φ = L/D = 2/√5 and cos φ = (L/2)/D = 1/√5 and (cos ⍺ sin φ + sin ⍺ cos φ) = √3 / √5 + 1/(2 √5), whence F_AB = (G/4) √5 / (√3 + 1/2) = G √5 / (4 √3 + 2).

Now the resulting force in A has horizontal component (sin φ) F_AB = G / (√3 + 1) and vertical component G/2 + (cos φ) F_AB = G/2 + G / (4 √3 + 2), from where you can get the direction / angle as arctan of their ratio. (Wolfram gives 30.88° for that)

You see that it isn't obvious to know the exact direction of the force in A without making the calculation.
But you could maybe indicate schematically a direction as vectorial sum of an arrow "G/2" going down from A and an arrow "F_AB" going from A in direction AB (but not equal to the length of AB).