You should not shadow the polygons that are back faced from the light.

I changed your fragment shader to below code.

float CalcShadowFactor(vec4 lightspace_Position)
{

    vec3 ProjectionCoords = lightspace_Position.xyz / lightspace_Position.w;

    vec2 UVCoords;
    UVCoords.x = 0.5 * ProjectionCoords.x + 0.5;
    UVCoords.y = 0.5 * ProjectionCoords.y + 0.5;

    float Depth = texture(inShadowMap, UVCoords).x;
    if(Depth < (ProjectionCoords.z + 0.001)) return 0.5;
    else return 1.0;
}

void main(void)
{

    vec3 Normal = normalize(pass_Normal);
    vec3 light_Direction = -normalize(light.direction);
    vec3 camera_Direction = normalize(-pass_Position);
    vec3 half_vector = normalize(camera_Direction + light_Direction);

    float fndotl = dot(Normal, light_Direction);
    float diffuse = max(0.0, fndotl) + 0.2;
    vec3 temp_Color = vec3(diffuse);

    float specular = max( 0.0, dot( Normal, half_vector) );
    
     float shadowFactor = 1.0;
    if (fndotl > 0.0)
        shadowFactor = CalcShadowFactor(lightspace_Position);

    if(shadowFactor > 0.5){
        float fspecular = pow(specular, 128.0);
        temp_Color += fspecular;
    }

    out_Color = vec4(shadowFactor * texture(inSampler, TexCoord).xyz * temp_Color, 1.0);
}

You should not shadow the polygons that are back faced from the light.

I changed your fragment shader to below code.

float CalcShadowFactor(vec4 lightspace_Position)
{

    vec3 ProjectionCoords = lightspace_Position.xyz / lightspace_Position.w;

    vec2 UVCoords;
    UVCoords.x = 0.5 * ProjectionCoords.x + 0.5;
    UVCoords.y = 0.5 * ProjectionCoords.y + 0.5;

    float Depth = texture(inShadowMap, UVCoords).x;
    if(Depth < (ProjectionCoords.z + 0.001)) return 0.5;
    else return 1.0;
}

void main(void)
{

    vec3 Normal = normalize(pass_Normal);
    vec3 light_Direction = -normalize(light.direction);
    vec3 camera_Direction = normalize(-pass_Position);
    vec3 half_vector = normalize(camera_Direction + light_Direction);

    float fndotl = dot(Normal, light_Direction);
    float shadowFactor = CalcShadowFactor(lightspace_Position);
    float diffuse = max(0.0, fndotl) * shadowFactor + 0.2;
    vec3 temp_Color = vec3(diffuse);

    float specular = max( 0.0, dot( Normal, half_vector) );
        
    if(shadowFactor > 0.9){
        float fspecular = pow(specular, 128.0);
        temp_Color += fspecular;
    }

    out_Color = vec4(shadowFactor * texture(inSampler, TexCoord).xyz * temp_Color, 1.0);
}