I'm not sure what you are trying to do. What do you mean by"able to upload Photos" -- from where to where, exactly?
Oh, I should look at your title! You mean in Safari you want to choose a picture from Photos to send to a web site--is that right Then I see-- the Photos picker doesn't allow you to navigate through albums and folders--something that's been crazy since Ventura, I think. It's a pain!
Selecting pictures and exporting them to the desktop is a method we suggest, because it gives you lots of control over the size and metadata of the transferred picture. So that's a good choice.
Another method is to use the search field:

I had an album named "25 07 07 Zoofari," and I copied that and pasted it into the search filed, so I got pictures from that album. I could also have just typed "Zoofari," but I would have gotten pictures from several trips.
You can also search for keywords. You can do the search in Photos and add a temporary keyword (like Safari?) to them, and do the search for the that.
I've done all those at one time or another…