I checked the Web Farm status and both the CMS and the MVC site are healthy.
Regarding the app_data folder, I remember seeing one at our blob storage under cmsstorage/app_data/cmsmodules/smartsearch though I'm not sure if that's the app_data you're pointing out.
But I also looked into the App_Data folder of the MVC site on my local machine and saw the CMSModules folder not included in the project. Inside it are three folders, CMSInstallation, SmartSearch, and WebFarm, all not included as well. Should I redeploy my project this time including all three folders in the project?