The problem you have is that the curtain rod will tear out the screw again. You
Can try a metal one but the drywall is already weaker there, it will rip out again.

If you’re in the mood to do it once here is what you do, it’s more work than you might be into.

1. Locate the studs to the left and right
2. Cut a square hole the width of a 2x4 and pull out the section of drywall.
3. Screw 2x4 into the studs.
4. Take drywall and screw it to the 2x4 so it is where it was before.
5. Get some drywall tape (I prefer the yelllow mesh for this type of job). And tape the perimeter of the hole.
6. Cover the drywall and hole with drywall joint compound, sand until smooth,repeat 3x until the wall is perfectly smooth.
7. Paint to match.

It’s about 2 hours to do it right, but it will last and be strong enough to withstand much more than drywall could.