Thank you for your reply @brbo and J_Johhnyboy. However I was looking for help in changing the function of the Gmail app notifications, not the Mail app notifications since I don’t use the Mail app.
In iPhone’s Settings > Mail > Accounts > Gmail, there are no swipe options or notification options.
After more digging around I was able to find that its possible to set those settings in the Gmail app.
Navigate to Settings under the hamburger menu (left), select Inbox Customizations > Mail Swipe Actions > select the option:
Archive, Trash, Snooze, Mark as read (Move does not work).
There is a left and a right swipe. Whichever two options are selected, those two will appear when a notification is long-pressed.
I hope this helps others who are looking for this setting.