I'd like to add.. it does seem to have a weeping habit.

I would suggest adding the Trees forum and the Name That Plant forum to your posting. Better close ups of the leaves would help too if you can get them. Things like leaf margins and shape are important for id.

Chinese elm (Ulmus parvifolia) from the bark pic.

I use an app called PictureThis which is awesome. I test it out all the time on plants that I already know what they are, and it is extremely accurate. You’ll just need a closer pic of the leaves

The bark resembles Chinese elm, but the leaves don't confirm.

It probably doesn't matter but where in SoCal are you? Palm Desert? La Jolla? Big Bear? Boron?

Picture This, like other apps, is not particularly reliable imo. Double check ids it throws up.