Inspect the gutters with the contractor (roof installer) and a flowing garden hose.

Leaking from the top can also be a sign of heavy rain and not enough downspouts, so the water backs up and flow over.

We had this issue in one section in front of our house. The one downspout could not handle the volume in that gutter section. We called the gutter company back to install one more downspout in that section.

1st image shows when they added an downspout. The leak is between the fascia and the gutter.

Did you pull off shingles to take those photos?

Did you check the downspouts? I've had gutters that look like yours (not full of leaves and sticks), but a clog at the top of the downspout. I used to keep a metal coat hanger around for pulling debris out of downspouts. Mark's garden hose test will show you where water is actually flowing.

Therefore that's what's causing the leak between fascia and the gutte ?

Maybe. If the drip edge installation was done wrong, what else may be wrong?

H/R shingle on the end looks short in addition to the drip edge question.

The downspout is dumping water next to the foundation. It would be better to move it away. Best to connect it to an underground drainage system with a popup at the end.

Did the roofer also install the gutters?

No, it was two separate contractors.