Hydrangeas and azaleas grow pretty big with good size root systems, and I’m not sure they are happy pot plants…? Not sure I have ever seen larger ones in pots.

I would not suggest azaleas (or rhodies) for containers - they do not thrive under those conditions - but hydrangeas are excellent container subjects!! As are many other broadleaved evergreen shrubs. And as I mentioned in your related thread about Japanese maples, containerizing the shrub is a natural dwarfing process, substantially slowing/restricting growth.

I'd visit a better local nursery and see what you like that fits the container sizes and your sun/shade requirements.

Sorry, you said rhododendrons, not azaleas. Rhododendron and hydrangeas don’t have really deep root systems, but if you want them to grow to 4 to 5 ft tall, I don’t see them happy in pots. Maybe small varieties of hydrangeas in pots, but only about 3’ max.

You can very easily grow full sized hydrangeas in containers - I have several that are approx. 5'x5'. And many other BLE's are well adapted to container culture and will reach 5' tall or more, as long as they are in a container properly sized to accommodate them.

I'm more concerned about the availability of light under cover.

Fwiw I've grown rhododendrons, azaleas and hydrangeas in large pots.