Answer: Birches tend to be healthiest and live longer in colder climates where winter are cold and summers are also cooler -- think New England. As a rule of thumb, the old saying is that the European birch does not do very well south of the Pennsylvania turnpike (unless you are high in the mountains), and although the B. jaquemontii seems to tolerate heat a bit better than that, it too would prefer a cool summer climate. Both also need a cool, evenly moist, organic and humusy, and acidic soil to grow well. Based on my experience, unfortunately, I would not recommend planting either of these.
Technically speaking, both are considered heat tolerant to summer heat zone 7 which is where your zip code places you; but keep in mind you are on the warmer end of their tolerance and a courtyard with reflected heat will likely be hotter than normal -- which would definitely be too hot for this tree.
Winter cold is also of concern, your zip code places you in USDA winter hardiness zone 7B, or the warmer part of zone 7. In a sheltered microclimate such as a courtyard with reflected heat it could actually be as warm as zone 8. These trees need winter cold to stay healthy, and winter hardiness zone 7 is the limit of their range. All in all I just could not recommend trying either of these trees.
Instead, if you truly want and have space for a birch, you might look at the river birch, Betula nigra. Its bark is not the silvery white, but does have wonderful peeling and plating texture. It may be too big for a courtyard, and it does have an extensive root system which makes planting around it difficult. (This is true of all birches.)
I would strongly suggest you consult with your local professionally trained nurseryman to analyze the growing conditions in your courtyard and based on knowing that, identify trees that would thrive there as well as fit into the space at maturity, then select the one you like best from those based on your design goals and personal taste.
Best of luck with your project!
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