'Switch to Salesforce Classic' Not Available after Upgrade from Essentials Edition

This is expected behavior. 

Salesforce Classic is only available to System administrators in Essentials Edition organizations. And it remains true after an organization upgrade. Standard Users only have access to the Salesforce Lightning Experience.

This access is linked to the "Modify All Data" system permission. Non-administrator Users who require the ability to switch to Classic must be assigned either a profile or a permission set that grants them the "Modify All Data" permission.

Also, the presence or absence of the system permission "Hide option to switch to Salesforce Classic" on a User's profile or via permission set has no effect on this behavior. 

Note: To make the Switch to Salesforce Classic option available again, submit a Salesforce Support Case under the Feature Activations & Limits topic with your org's emergency justification. Request to disable the 'Users are Lightning Only' perm to give your standard users the ability to switch to Salesforce Classic.
 

See Also:
About the 'Modify All Data' permission
Make Lightning Experience the Only Experience for Some Users
Toggle or Switch between Lightning and Classic
Turn off Salesforce Classic for your org
Things to be aware of if you don't allow users to toggle between Lightning and Classic