Nothing tree-like :-) Here, bearded iris are in bloom around Mother's Day - early May. The crabapple will have already bloomed and should/will be in full leaf by then. I can't think of many trees that would not be.

Here, bearded iris get the absolute sunniest spot I can find for them. If you want to plant anything that blocks sun, plan on moving the iris.

So what if I built a pergola on that side of the house? I would plant a summer-blooming clematis to grow on the pergola.

As long as whatever you decide to do does not create more shade for the iris than now exists, you should be fine.

OK, the pergola will probably create some shade so I guess I will forget it. Thanks!