Your concerns and caution are a good thing. You should be taking 2FA slowly and only when you are comfortable with it on a given service.
I'm glad that you seem to be successfully using Apple's 2FA implementation. It's makes your account far more secure than without it.
As far as Google accounts, here is a bunch of information about how it works:
https://support.google.com/accounts/topic/7189195?hl=en&ref_topic=3382253
In it's simplest form, you will install the Google Authenticator app on your iPhone. Then, during the process of enabling 2FA, you will be walked through adding your Google account to the Google Authenticator app. Once added, your Google account will be listed in that app along with a 2FA code that is listed for 1 minute before a new code is generated and the cycle repeats. Once 2FA is enabled on your Google account, you will login to Google from a browser like you always have, but will then be prompted for a 2FA code. You will then open the Authenticator app on your iPhone, read the current code for your Google account, and then type it into the browser to complete the login. You can also choose to "trust" the computer for a while so you don't need to do that every time.
During the process of enabling 2FA for Google accounts, you will also be prompted to create several special application specific passwords to use when setting up your Google accounts in email clients like the Mail app on your phone. You will substitute the application specific password for you actual password in the Mail app settings on your iPhone. The benefit of these special application specific passwords is that if you ever lose your iPhone, you can log into your Google account using a web browser, and then cancel the application specific password that is used on your phone.
Yes, it is confusing. But if you read through their information you may eventually feel confident enough to enable it. You will then find that it's not as cumbersome as you think, yet is adding significant security to your Google account or any other account. Lastly, once you have used the Google Authenticator app for one service, you will find that many other services allow the same app for their 2FA implementations. I currently have over a dozen services in my Google Authenticator and it works the same for all of the services -- login normally using a username and password, and then get prompted for a 2FA code before the login can be completed.