Hi Mindy, I have two experiences with lonicera.
I have lonicera heckrottii Gold Flame on a stone wall, and it is very bushy. It sends out long tendrils which if given assistance would love to climb up something. It grows well on the shaded side of the wall, too though it is not so vigorous.
I trained Major Wheeler (I don't know if that is a heckrottii) up a heptacodium, which unfortunately grown into a tall, multiple stemmed bushy tree. It took nearly 3 years to get established. It got south sun for several hours a day. I did not find it very effective, but it really didn't have a chance to get lush before I took down the ugly tree and it along with it.
I got the idea from a garden tour where the owner had limbed up tall heptacodiums (I bet they were 20-25 feet) and trained Major Wheeler honeysuckles up the trunks. I thought it was a very clever reference to the tree's 'flowers' that would bloom in a month or so. They were not lush, but it was an idea that worked. It was a pretty open location.
By 'shady side' if you mean dark shade then your bloom will be
sparse. But lonicera will take some shade, for sure. And it wouldn't mind the dry-ish soil shared with your hydrangea p.