Ask ten authors whether you need an ISBN and you will get ten confident answers, most of them wrong in some detail. The truth is less dramatic: an ISBN is a tool for a specific job, and whether you need one depends entirely on who you expect to order your book.
What an ISBN actually does
An ISBN (International Standard Book Number) is a 13-digit identifier for one edition of one book in one format. Its job is to let the book trade talk about your book without ambiguity. A bookstore's ordering system, a wholesaler's warehouse and a library's catalogue all key on it.
That is all it does. It does not protect your copyright, it does not register your title with anyone who markets it, and it does not make your book discoverable on its own. It is a part number.
Where you do need one
Bookstores and libraries. If a bricks-and-mortar shop or a library might order your book, you need an ISBN. Their systems cannot order anything without one, and a wholesaler such as Ingram will not list a title that lacks one.
Print distribution through wholesalers. IngramSpark and similar services require an ISBN for every print edition they distribute, because the stores they feed require it.
Some ebook retailers and aggregators. Apple Books, Kobo and most aggregators ask for one, though several will assign a free identifier if you do not have your own.
Where you do not
Selling direct. Your own website, your table at an event, a box of books sold after a talk: none of these involve the book trade's systems. No ISBN is needed.
Amazon Kindle ebooks. Kindle titles use Amazon's own ASIN. An ISBN is optional and, for ebooks, rarely worth the money.
Amazon KDP print. KDP will assign a free ISBN to a paperback or hardcover. The catch: that number lists "Independently published" as the publisher and cannot be used with any other printer. If KDP is your only print channel, it may be enough.
Zines, chapbooks, workbooks and comics sold at events rarely benefit from one at all.
The question to ask yourself
Not "is my book real without an ISBN?" (it is), but "will anyone need to order it through a system that requires one?" If the answer is yes, buy the ISBN before you print, because it goes on the cover. If the answer is no or not yet, you can add it later with a new print run.
What you need regardless
Whatever you decide about the ISBN, every printed book benefits from three things: a barcode that scans, a page online that stays current, and some way of knowing whether the book is reaching anyone. None of those require an ISBN, and none of them come with one.
That is the gap ScanSpine fills. Register your title and you get a scannable QR code, a barcode and a hosted page immediately. If you have an ISBN, add it and the barcode becomes the official retail format. If you do not, you still have everything you need to sell direct and learn from it.