[WhatsApp] Cannot setup backups / MicroG stuck on a loop: "Account Already Exists"

App Name: WhatsApp

I encountered this bug when trying to setup WhatsApp backups to my Google Drive. But I don't think this bug is specific to WhatsApp. It looks like a repeat of #1403 and #1847.

Steps on WhatsApp:

1. Go to WhatsApp > Settings > Chats > Chats backup
2. Under "Google Account" it says "None selected".
3. Click on "Google Account".
4. New page says "microG Services Core".
5. Click on "Sign In"
6. I get a Google sign in page. Enter email & password & 2FA.
7. Login successful, "please accept terms and conditions". Click "I Agree"

After this I am back to the WhatsApp chat backup page, but no Google account is selected.

1. Click on "Google Account" again.
2. Click "Sign In" again.
3. Enter email again.
4. Error: "This account already exists on your device."

If I go to system settings > passwords & accounts, I can see the Google account listed. If I delete the Google account I can go back to WhatsApp and try steps 1-7 above, and I get the same result. In the end, no google account is selected.

Steps without WhatsApp:

1. Go to microG settings.
2. Under Accounts it says "Add Google account".
3. Click on Accounts.
4. I get the same "Sign in" page from microG that I saw from WhatsApp.

Same error occurs:

1. Click on "Sign In" again.
2. Enter email again.
3. Error: "This account already exists on your device."

System:
Android Version: 13
Custom ROM: Calyx OS 4.11.0

microG:
microG Core version: 0.2.25.223616-76
microG Self-Check results: All ticked

Reproduce the flow from microG settings > Accounts and the WhatsApp Chats backup page on Android 13, then compare the behavior with issues #1403 and #1847. Done means an account can complete sign-in and terms acceptance, appear in microG accounts, and be selectable for WhatsApp backups without the "account already exists" loop.