We ran into exactly the same problem - Shopify hasn't documented the Shopify data elements that contain size (aka Package) dimensions used to create a label in Shopify Order fulfillment. We called guru support. They told us to post here (see link below).
We then started searching on "Weight and Size" as the Shopify UI refers to "package" size by those terms as well and found your post.
We also tried
--Reviewing Shopify online data dictionary for an element name - nothing published,
--pulling up the .json for orders - not listed,
--inspecting the "package" size UI elements - not named,
--viewing page source for "package" size elements - not named,
--asking for guru support to ask technical support - told it was "out of scope",
--Shopify webhooks, notifications and api - found nothing,
--Searching and posting on Shopify Forums - no answers but found your post.
If Shopify could please support this very basic piece of data, that is What Size Package was the order label fulfilled with?, that would be very helpful.
As an acceptable solution (for me), I've since gone solely with Pirate Ship, which is an outside solution that integrates with Shopify. From it, I can get reports with all my shipment info, which is tied to my shopify order ID. It also has the added benefit of offering USPS Priority Mail Cubic, which tends to be less expensive. It only ships through USPS though, which may be problematic for some.
Fields in the shipment report:
Estimated Delivery Time
Address Line 1
Address Line 2
Rubber Stamp 1
Rubber Stamp 2
Rubber Stamp 3
This isn't intended as an advert for Pirate Ship, though I do like the service.
I still wish Shopify would make this info available for those who don't want to employ a third party service.
Just in case you don't know, shopify now offers USPS Priority Mail Cubic Shipping. I think they started to do this last Winter (2018) or this Spring (2019). Also, Shopify negotiated for a general Shopify discount for USPS and UPS using all Shopify accounts to get a single large "scale" discount for any Shopify Merchant who sets it up in Shopify. So now the label discount is as good as that on eBay (if you're familiar, it is an excellent discount)
So in the Shopify order label creation step now, Shopify will offer you the best price for UPS, USPS, and USPS cubic shipping. It is up to you (the merchant) to understand cubic shipping T1-T5 levels, but if the box sizes you use meet those USPS cubic shipping size requirement, you get a great label price with significant discount. I suggested last year Shopify auto calculate if a box size matches t1-t5 and label it for Merchants because why wouldn't you?
That said we've kept our solutions Shopify in the core (without porting large amounts of data out to third party apps) in order to avoid the pitfalls therein. So we search for apps that integrate with Shopify, rather than suck all the data out and recreate the wheel (Hello MailChimp). That said we're working with the developers of FedEx Rates, Labels & Tracking App as they're willing to integrate FexEx as well into the Shopify Order screen...currently in beta.
So we still really need that Shopify data element for the fulfillment-package-size. (Weight would be nice too, but we want package size to clue our warehouse into what box to pull.) Interestingly shopify currently places weight on all labels that use weight, but ONLY PUTS PACKAGE SIZE ON UPS LABELS and NOT USPS Labels. Hence the need.
Thanks again, glad to trade app favorites here and wishing you the best.
To anyone else reading this, if you know the shopify data element name for the fulfillment-package-size you will have us in awe if you can find it!