I don’t use iOS, so I can’t speak to it directly, but some quick searching tells me it supports IMAP, caldav, and carddav. If so, you could just use native apps.
Most of the privacy respecting email services require a paid plan for this, but they are inexpensive.
This doesn’t solve your Google calendar ask, but I pointedly don’t have my work calendar on my phone. I just check each calendar separately when needed, it’s not much extra work.
I imagine a good number of people will fall for this. Tech illiteracy is the norm.