In production under activity there are two items, new task and email. In sandbox I pull the same Email (send email) to the Salesforce Mobile and Lightning Experience Actions in account page layout, save it, but still it doesn't show up under the activity. I am able to add other actions like log a call, but not sure what's wrong with Email. When I go back to Account page layout I don't see the Email in the Salesforce Mobile and Lightning Experience Actions, as if I hadn't dropped it there.
You might need to check the email Deliverability to make it All Email. If it is not set to email Deliverability, It will not come on the layout and Every time you add the email action on Mobile and Lightning Experience section, As soon as you click on save it will get removed automatically from the page layout.