Photos in icloud library not going to phone

[mizzourah]

I am not sure if this is in the right place, but I do not know where else to post.

I do not understand the photos app and how photos get to and from my phone - I am utterly confused.

I have icloud library turned on and so pictures I take on my phone get to my ipad. Great. But I have pictures on my computer that I would like to get on my phone and I cannot just synch them like I used to.
So, I have imported those pictures into the Photos app, presumably, they get uploaded to the cloud and then appear on my devices. But they don't. They aren't there. I see them in Photos, but not on my phone.

And then, in reverse, how do I get these pictures off my phone - I don't see how that works, within Photos.
For the first time, I am so confused by the way Apple is handling things, and that it is about my pictures, which are my memories, my life, it bothers me.

I have searched hi and low on the internet to try to find my answer, but all the writeups make Photos sound so easy - is there any insight..any solution on how to get regular pictures on my computer to my phone, since I can't synch them due to icloud library.

Thanks to anyone who has any insight.