I only use Google contacts and email accounts for all my devices but here is what I got when I asked Gemini.
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To successfully sync your Apple Mail, Calendar, and Contacts with an Android device, the most critical step is generating an App-Specific Password through your Apple ID account. Standard iCloud passwords will fail when you try to log into Google apps.
Here is how to set up each service on your Android phone:

Step 0: Generate an App-Specific Password
Go to apple.com and sign in with your Apple ID.
Navigate to Sign-In and Security and select App-Specific Passwords.
Click Generate an app-specific password, label it (e.g., "Android Mail"), and copy the unique password provided.

1. Apple Mail in the Gmail App
The user in the image mentioned having issues setting this up. The trick is choosing the correct account type:
Open the Gmail app on your Android phone.
Tap your profile picture in the top right and select Add another account.
Choose Other (do not select iCloud, as it often causes sync loop errors in Gmail).
Enter your iCloud email address.
When prompted for the password, paste the App-Specific Password you generated in Step 0.

2. Apple Calendar
The Gmail/Google Calendar app on Android does not natively support iCloud calendar syncing out of the box without third-party help. You have two main options:
Option A (Sync directly with an app): Download a highly-rated sync utility app from the Google Play Store, such as Sync2 iCloud or DAVx⁵. These apps run in the background to seamlessly sync your Apple Calendar directly into your native Google Calendar app using your App-Specific Password.
Option B (Public Link - View Only): If you only need to see your family's calendar, open iCloud.com on a computer, go to Calendar, click the share icon next to the calendar, check Public Calendar, and copy the link. Paste this link into Google Calendar (Web version) -> Add Calendar -> From URL.

3. Apple Contacts
Android requires a dedicated account link to sync iCloud contacts natively.
Go to your phone's main Settings -> Passwords & Accounts -> Add Account.
Look for iCloud or Exchange (depending on your phone manufacturer).
Enter your iCloud email and your App-Specific Password.
If your specific Android flavor doesn't support this natively, you can use the DAVx⁵ app mentioned in the calendar section to sync both contacts and calendars simultaneously via CalDAV/CardDAV protocols.
Would you like step-by-step instructions on how to set up DAVx⁵ to handle both the contacts and calendar sync at the same time?