Limits of my camera and lens?

There is a lot to consider when imaging the night sky. Obliviously, your equipment has limits, but there is a lot out of your control.

To my eyes, the leaves look in focus (or close to in focus) and therefore you probably have a depth of field problem in these images. Or atmospheric haze could be degrading the image of the moon as well. But there is more to deal with than that.

I found this thread on shooting the moon:

https://www.dpreview.com/forums/thread/3684935

It seems to have a lot of good suggestions. Taking good images of the moon is more difficult than you would think. The apparent motion of the moon and stars is faster than you perceive when looking up. The dynamic range of a bright moon and a dark sky adds complications as well. Spot metering is called for and even then bracketing is necessary. You will still have a lot of throwaways. In addition there is often fog or haze and light pollution that must be dealt with. Here in the Atlanta area I find the best evenings to shoot sky pictures typically are in the winter. There is much less haze producing ozone in the atmosphere since plants are not growing and the relative humidity is typically lower. A clear, chilly night in 30's (or lower) Fahrenheit with steady light winds seems best.

Using a tripod helps, but it is really not hard to do handheld. I usually don't use one on the moon.

I put my equipment in ziplock bags to cool down outside before shooting and warm back up after shooting. This cuts down on condensation. This is especially important when coming back inside. Dampness is not the camera's best friend.

Here is a good discussion of shooting the night sky in general:

https://shuttermuse.com/how-to-avoid-star-trails/

There is a lot of information online about this. Just do searches on what you are looking for.

Hope this helps.

Glenn