There are several ways of interpreting your ask...
> I am trying to set up a recurring meeting in the Google Meet website. I would like to enter it in my Apple Calendar but I only see the option for Google Calendar
When you create a meeting in Google Meet, it adds it to your Google calendar that's associated with your Google Account. That's always been the case.
If you want to see your calendar in Apple's Calendar.app, then you need to connect Calendar.app to your Google account. That way all your Google Calendar events will appear in your Apple Calendar (and you can schedule events in Apple's Calendar.app that populate through to Google Calendar.
To set this up, just open Calendar.app and choose the Calendar -> Accounts menu option.
You should see a list of internet accounts that are configured on this system. One of them should be your Google account. If it is, click it to expand, and make sure the Calendar option is enabled. Now this will add a new Calendar to your Calendar.app showing the events in your Google Calendar account.
If your Google account is not listed, just click the Add Account button and follow the prompts to setup your Google Account, and choose which services you want to use (e.g. Mail, Contacts, Calendars, etc.)
I can't help with the contacts question, though... it may depend on how the contacts were synched
