How do I choose a HTTP status code in REST API for "Not Ready Yet, Try Again Later"? [closed]

I suggest 202 - Accepted. From the documentation:

The request has been accepted for processing, but the processing has not been completed. [...] Its purpose is to allow a server to accept a request for some other process (perhaps a batch-oriented process that is only run once per day)

The "problem", such as it is, is on the server side: the client has made a well formed request, but the server can not satisfy it. So I'm inclined to a "Server Error", 5xx status code.

Quoth RFC 7231 (the current HTTP standard, emphasis added):

The 5xx (Server Error) class of status code indicates that the server is aware that it has erred or is incapable of performing the requested method. Except when responding to a HEAD request, the server SHOULD send a representation containing an explanation of the error situation, and whether it is a temporary or permanent condition.

Note

• "erred or is incapable of performing the request": despite their title of "Server Error", they are not just for server errors.
• "temporary or permanent": these codes are suitable for temporarily unavailable resources, like yours.

Of the available codes, I'd say 503, "Service Unavailable" was the best fit:

The 503 (Service Unavailable) status code indicates that the server is currently unable to handle the request due to a temporary overload or scheduled maintenance, which will likely be alleviated after some delay. The server MAY send a Retry-After header field... to suggest an appropriate amount of time for the client to wait before retrying the request.

Note:

• "likely be alleviated after some delay": true for your case.
• "temporary overload": not pedantically true for your case. But, it could be argued, were your server much faster, the batch processing would have already been done when the client made the request, so it is a kind of "overload": the client is asking for resources faster than the server can make them available.
• Retrying is suitable for your service, so your reply ought to include a Retry-After value. You could provide as the value the estimated completion time of the next execution of the batch process, or the execution interval of the batch process.

Defining your own 5xx status code (591, for example), although permitted, would have the wrong semantics:

a client MUST understand the class of any status code, as indicated by the first digit, and treat an unrecognized status code as being equivalent to the x00 status code of that class

Clients would treat your own status code as 500, "Internal Server Error", which would not be right.

I think that 423 - Locked can be used for this purpose:

The 423 (Locked) status code means the source or destination resource of a method is locked. This response SHOULD contain an appropriate precondition or postcondition code, such as 'lock-token-submitted' or 'no-conflicting-lock'.

I don't want to return 404; that's for thingies that do not exist.

The URL doesn't correspond to a request for a thingy.

http://server/thingyapi/thingyblob/1234

The client is requesting a thingyblob, which doesn't exist. If it existed, you would give it to them.

404.