Glad you found that helpful! Also happy to hear you are doing work for them again.
I haven’t ever worked for a publisher, but I do periodically reach out to authors who I know plan on writing more than one book.
I usually say something like “I enjoyed working on your first book and am wondering if you have any more books in the works. I currently have openings around this time. If you have any immediate future plans for a book, let me know, as I would love to prioritize your book.”
With a publisher, I imagine you could say something like “I am just reaching out to see if you have any work for me within the next month as I currently have some openings.”
That way, you are reminding them of your services and expressing an interest in doing more work for them without seeming desperate or demanding.