I wrote an answer on it here

As you said, you want WorldToScreenPoint or whatever, but you also want to use GetPartsObscuringTarget.

Edit

What you actually want is "Character facing towards part", not "Player looking at part"

You can do this with vectors:

player = game:GetService("Players").LocalPlayer
character = player.Character or player.CharacterAdded:wait()
torso = character:WaitForChild("Humanoid").RootPart
target = workspace:WaitForChild("LookyLou")
vectors = {}


function dotProduct(a, b)
    return a.x * b.x + a.y * b.y + a.z * b.z
end


function getAngle(a, b)
    return math.acos(dotProduct(a, b) / (a.magnitude * b.magnitude))
end


function drawVector(position, angle, magnitude, name)
    if vectors[name] then
        vectors[name]:Destroy()
    end

    local p = Instance.new("Part")
    p.Anchored = true
    p.Size = Vector3.new(0.1, 0.1, magnitude)
    p.CFrame = CFrame.new(position + angle * magnitude / 2, position + angle)
    p.CanCollide = false
    p.Parent = workspace

    vectors[name] = p
end


game:GetService("RunService").RenderStepped:Connect(function()
    local torsoAngle = torso.CFrame.lookVector
    local targetVector = torso.Position - target.Position
    local flatTorsoAngle = Vector3.new(torsoAngle.x, 0, torsoAngle.z)
    local flatTargetVector = Vector3.new(targetVector.x, 0, targetVector.z)
    drawVector(torso.Position - Vector3.new(0, 2.5, 0), flatTorsoAngle, flatTargetVector.magnitude, "torso")
    drawVector(target.Position, flatTargetVector.unit, flatTargetVector.magnitude, "target")

    local angle = math.deg(getAngle(-flatTorsoAngle, flatTargetVector))
    if angle > 40 then
        target.BrickColor = BrickColor.new("Bright red")
    else
        target.BrickColor = BrickColor.new("Bright green")
    end
end)

Put a brick in the workspace called "LookyLou" -- it will go red when you're within 40 degrees of facing it.