How do I add my own entries to the new Windows 11 right click context menu?

Is there a new Windows 11 API for this or something?

No, not yet. Windows 11 is still pre-release so we don't know for sure yet.

One attempt here a month ago or so attempting a registry change failed at one of the Windows 11 updates.

I suggest you enter your request in the Windows 11 Feedback Hub. I got a lot of positive feedback for requesting context changes: What you are looking for and right click off the task bar - both items.

But in direct answer to your question, change the right context you displayed is not possible at this point in time.

Note however, that the new Windows contexts have grown to include correct key icons where appropriate, that is, the context menu is not fixed. This means the Windows 11 context design is a little more intelligent than the older way with a very long context.

So first, in one folder, I copy.

Now in the second folder, I paste. Notice the Paste icon in the key row (bottom in this operation) and that is just what I need to do. So some things are addressed in the new Windows 11 design. Paste occurs where it is needed, not always alongside cut and copy.