Do rainbows only occur after rain has fallen or can they be formed alongside other weather types?

Rainbows can be observed whenever there are water drops in the air and sunlight shining from behind a person at a low altitude or angle (on the ground). The most spectacular rainbow displays happen when half of the sky is still dark with draining clouds and the observer is at a spot with clear sky in the direction of the Sun. The result is a luminous rainbow that contrasts with the darkened background.

The rainbow effect is also commonly seen near waterfalls or fountains. Rainbow fringes can sometimes be seen at the edges of backlit clouds and as vertical bands in distant rain or virga. The effect can also be artificially created by dispersing water droplets into the air during a sunny day. Rarely, a moonbow, lunar rainbow or night-time rainbow, can be seen on strongly moonlit nights. As human visual perception for colour is poor in low light, moonbows are often perceived to be white.

https://en.wikipedia.org/wiki/Rainbow

Here is an awesome photograph of a moonbow:

https://sciencemadefun.net/blog/the-science-of-moonbows/

All aerial bows are a result of light refracted by suspended water particles. They are observationally specific and directional.

http://eo.ucar.edu/rainbows/