Your custom theme template is working exactly as a WordPress theme template is meant to work. The template is used to render what you put into the post editor. But the template itself is not editable in the post editor.
As you need to edit this “template” for every post (event), a custom theme template is not what you need.
A better out-of-the-box solution would be the “Reusable Block” feature: you create a block or group of blocks with all the presets you need and save it as a Reusable Block. Then for every new post (event), you insert this Reusable Block and customize it.
One caveat with the Reusable Block feature is, by default, editing a Reusable Block will edit ALL posts where you inserted this particular Reusable Block. But there’s an easy solution to that: after inserting the Reusable Block you want to use, make sure to select “Convert to Regular Block” option and your changes will affect that particular post (event) only.
Good luck!
Reusable Blocks
Thank you George, that’s really helpful; I suspected I was going about it the wrong way.