Ok, I think I figured it out. Since it's a work phone, my company required the addition of MobileIron/Apps@Work, and those are somehow preventing the use of keyboards downloaded directly from the AppStore. I’m drawing this conclusion because I found swiftkey in Apps@Work, and after downloading it from there, it showed up as a keyboard option in mail. Gboard still doesn’t show up in mail, so that must be issue.
To make sure I tried everything to get gboard to show up in mail, I restarted the phone, but it still wasn’t there. Finally, I checked on my daughter's iPhone 14, and her mail app shows all the 3rd party keyboard options. So it’s the MobileIron/Apps@Work.
As a final bit of annoyance/nuisance, I’m typing on gboard right now(in Safari), but swiftkey isn’t an option. Such a ridiculous mess, but it’s caused by my employer. Thanks for responses!