Tukukkk

I am trying to add custom fields to the "New Event" layout under "Activities" on Opportunity:

However, it appears this component is a static, non-customizable component because when I click on it in Builder, I only see this:

One forum post suggested that one cannot customize this component and therefore cannot add custom fields.

Another post suggests it is possible by editing the Global Action Layout, but this only changed the Global Action for Classic UI.

How can I make available a custom "New Event" layout in Lightning Experience under the "New Event" tab?

You can't edit the Activity Publisher component, but you can change the set of tabs that appear therein. They're Quick Actions.

You can control which Quick Actions appear in the Activity Publisher by editing the "Lightning and Mobile Quick Actions" section of the page layout assigned for the relevant record type/profile combination. It's not editable from Lightning App Builder.

Note that the Lightning and Mobile Quick Actions section is "digested" by the Lightning Experience to generate both the Activity Publisher tabs and actions that appear in the button bar on the record page. Actions that publish Activities (Events and Calls) will automatically be routed to the Activity Publisher, and will appear in the same order they're shown in the Lightning and Mobile Quick Actions section.

You can create new Quick Actions, and edit existing ones, in Object Manager. Edit the Quick Action Layout to add or remove fields from display, or add Predefined Field Values to prepopulate fields whether or not they're shown on the layout.

When you want to add a custom field in the new event tab inside activities on lightning record detail page layout, First check the button, link and action section under object manager of an object if there is any new event quick action or not. If there is not, then the new event action is a global action.

In order to add an extra field on global action layout, you can go to setup and type global action and select and open the new event action and edit the page layout. Add the desired field to the new event global action layout.

Note:- Any change in Global action will reflect everywhere it is being
used. If it affects your org, My suggestion would be to go and create
one object-specific quick action of type create a record and select
target object as the event. Add the desired field on the layout of the
action.

Using Global action on the layout and having record types for the event
and task in your org needs one extra activity. You need to associate a
record type for global action in order to show those actions under the
activity tab on the record page in lightning. If you do not, even
after adding the global action in salesforce mobile and lightning
action section on the page layout, the action will not appear in
activities tab.

One good solution if you want to use the related list to create New event and the task is:-

1. add related list single on the layout by editing the page using edit page option appears after clicking the setup icon


2. 
   

   select the object Open activities and save it. Do not forget to activate it.

   
   
   

   Once done, In your related list, You can see the open activities related list as you were seeing it in Classic. Even You can add this one inside Activity publisher tab on the lightning record detail page. The field displayed here are controlled by normal page layout for task and event. Refer How can I customize my tasks and events page layouts? for more information to edit the page layout of an event and task.

   
   

The advantage of using related list is the button here will give you
an option to select the record type which will never possible through
an action. Action always needs to associate with a record type, hence lose the ability.

This image tells you about related list single:-

This image tells how you can edit the event layout when using related list single:-