In case anyone else experiences this, I thought I would share the methods I used to resolve the crashing issue. The issue was not a manifestation of updating my iOS back in May. This was a sudden crashing issue.
First, I'd like to clarify that I'm not actually an idiot, and do know that the Google app is not one developed by Apple.
Secondly, I did not need to resort to the draconian measures that were recommended. I actually know how to back up my iPhone to both iCloud and my iMac. I also know how to restore from backup.
My steps (gleaned from an assortment of solutions found via Google searches):
Deleted all Google apps from my iPhone.
Deleted the Gmail account from my iOS Mail app.
Turned off and restarted iPhone.
Added the Gmail account back to my iOS Mail app.
Turned off and restarted iPhone.
Confirmed that Gmail account was functioning properly in the iOS Mail app.
Reinstalled the Google app.