If the Multiplayer button is grayed out due to account settings, check your Microsoft account permissions first. In the family account, the authorized adult changes the setting.
Step by step
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Verify that you're signed in to Launcher with the correct Microsoft account. Open your account settings from the same account as the account running the game.
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Check permission to join multiplayer games in your Xbox privacy and online safety settings. If you're going to play cross-platform, also check the relevant permission.
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If it's a child account, the family organizer must edit the permission by logging in with their account and selecting the correct player profile.
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After saving the change, exit Launcher and log in again. If the menu opens but you cannot access a single server, check the address, version or whitelist status of that server.
Keep in mind
Online permissions do not change a Minecraft server's own ban and whitelist rules.