Tides depend on both the moon and sun. So does the phase of the moon.

Tides are largest at full moon and new moon, when their gravity gradients combine to enhance each other's tides. A week later, their gravity gradients interfere, decreasing the amplitudes of the tides.

Moon phase is caused by moon position.

Moon phase is caused by moon position, relative to the sun-moon-earth system.

My point was that the moon can be directly above or below, regardless of phase.

.... but thinking about it a little more, the tide probably gets an additional boost when the sun is contributing (i.e., the 3 bodies are lined up)

It's commonly known as a spring tide:

https://oceanservice.noaa.gov/facts/springtide.html

It's readily apparent along most coasts.

Aside, grew up in Florida and was always a little surprised whenever I met someone who'd not seen the ocean until they were an adult, but eventually realized maybe that wasn't so odd considering I didn't see snow for the first time till I was an adult. To me, skiing is something you do on the water, so when I say "snow skiing" people often look at me oddly, as if there's any other kind. Well, there is. :-)

I have been told by a friend of a student from Louisiana who was an avid water skier. Her friends at UC Berkeley discussed going to the lake to ski. She joined and was quite confused by the snow on the ground.