Contact synchronization fails with ServerError

Describe the bug
Contact synchronization doesn't work with such errors in logcat:

05-21 19:09:53.180  3464  3582 D GmsAuthenticator: getAuthToken: Account {name=***REMOVED***, type=com.google}, cp, Bundle[{androidPackageName=com.google.android.syncadapters.contacts, callerPid=3775, callerUid=10209, notifyOnAuthFailure=true}]
05-21 19:09:53.907  3464  3582 W GmsAuthenticator: java.io.IOException: Error=ServerError
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at org.microg.gms.common.HttpFormClient.request(HttpFormClient.java:95)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at org.microg.gms.auth.AuthRequest.getResponse(AuthRequest.java:195)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at org.microg.gms.auth.AuthManager.requestAuth(AuthManager.java:233)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at org.microg.gms.auth.loginservice.AccountAuthenticator.getAuthToken(AccountAuthenticator.java:97)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at android.accounts.AbstractAccountAuthenticator$Transport.getAuthToken(AbstractAccountAuthenticator.java:244)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at android.accounts.IAccountAuthenticator$Stub.onTransact(IAccountAuthenticator.java:282)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at android.os.Binder.execTransactInternal(Binder.java:1159)
05-21 19:09:53.907  3464  3582 W GmsAuthenticator:      at android.os.Binder.execTransact(Binder.java:1123)

Calendar synchronization works at the same time.

To Reproduce
Steps to reproduce the behavior:

1. Enable contact synchronization

Expected behavior
Contact synchronization works

System
Android Version: 11
Custom ROM: LineageOS 18.1, Phh-Treble

Additional context
I installed microG via NanoDroid, synchronization apks via NanoDroid using Q ones. When I faced this error, I updated microG to the latest version from GitHub releases (0.2.19) via adb install and replaced synchronization apks with ones from OpenGAPPS test archive (Pico). As you can see, that didn't help :(.

Start with org.microg.gms.common.HttpFormClient.java at line 95, then follow the request through org.microg.gms.auth.AuthRequest.java, AuthManager.java, and AccountAuthenticator.java as shown in the log. Reproduce the failure with contact synchronization enabled on the reported Android setup and compare it with the working calendar synchronization. Done means contact synchronization completes without the ServerError.