Your climbing hydrangea looks like it might recover.  Water it deeply in dry periods.  We do not see any evidence of any need for spray or treatment.  If the hydrangea dies, you could have a soil test,  then follow soil test recommendations and dig a deep hole and incorporate organic material into the soil.  It is not uncommon to have spots in the yard that seem to be deathly to plants.  Sometimes it is just coincidence, improper planting or watering and rarely is it a localization of some kind of toxic material.  For example a previous owned could have dumped wood ash in that spot and the soil could be too basic.  It is possible that this corner is a low spot and water stands there.  https://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG86%20Common%20Abi...

https://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG24_Planting_tips_...  vw