Hi there, this is Marc. Thanks for reaching out to the community.
The sign-in loop with Microsoft Store usually happens because of corrupted cache or credentials. Start by clearing the Store cache with Win + R > wsreset.exe, then try signing in again. If that fails, reset the Store app under Settings > Apps > Microsoft Store > Advanced options > Reset.
Also check that your date and time are set automatically, since wrong settings can block sign-in. You can also run the Windows Store Apps troubleshooter, remove old Microsoft account entries from Credential Manager, or re-register the Store with PowerShell using this command:
Get-AppxPackage -allusers Microsoft.WindowsStore | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}
If the issue continues, try creating a new user profile or running system scans with sfc /scannow and DISM /RestoreHealth.
Best regards,