These page describes common errors with authentication. If the specific advice doesn't help, try either deleting and adding the account again into the mod or logging in via vanilla launcher.
If this page doesn't help you, feel free to ask for help via Discord.
Your internet is not working properly or your ISP or region or country is blocking Microsoft and/or Minecraft. Try checking your internet connection (especially to microsoft.com or minecraft.net) or try using vanilla launcher to log in first.
You've probably opened previous authentication page or did something similar. Try fully closing your browser and performing authentication once again. If this didn't help, try a different browser.
You've closed the authentication page. Try again. If you didn't do this, possibly you're being restricted by your family control.
You've entered the wrong decryption password or your hardware has been changed. Try entering the password again or remove and add the account.
You're probably selecting an account which doesn't own a game. If that's not the case, try adding this account into the vanilla launcher.
Microsoft and/or Minecraft is not available in this region. If it should be available, check if you don't have any VPN or proxy enabled.
Current family control settings or Microsoft policies require approval by an adult. If you don't have any family policies, or you're over 18, check your age in the Microsoft account settings.
You're probably selecting an account which doesn't own a game, or you've selected an account with the Xbox Game Pass which requires setup through vanilla launcher. Anyway, try adding this account into the vanilla launcher.