Yes, and StayGo manual is noting: “using the laptop’s USB-C power adapter (after deduction of 15W used by the hub). USB-C power adapter not included.” So here is my understanding of it (this community might help further): this manual talks about using of for particular laptop provided 20/2.25, 20V/3A, etc. charger and we (you) don’t want to charge this hub with any of USB-C 20V (me neither) charger (like that) in direction of Librem 13v4 (as not supposed to do/provide such pass-through as well).
As next this manual mentions “15W”, so I’d (you) take some simple smartphone charger that provides only 5V/1.5A. If such not available you can choose one with up to max. 5V/3.0A (which equals 15W). Even those that support 9V/2.0A and 12V/1.5A might provide enough current for your hub but do not damage your particular laptop, please (on your own risk). Please take a look at DeLOCK 64054 manual and you’ll see that it is delivered with charger which output equals purposely to 5V/2A (5V only). Anyway, my main concern/idea, what I’m writing here, is that your source charger (perhaps 5V only) should not provide to the hub and therefore in direction of your laptop more than 12V and certainly not more than 15V, nothing (preferably less), nothing stronger than something like this charger should you test (in offline mode first). (NOTE: Even USB-C PD powered laptop would not recognize 12V or less to power itself on.)
Without further explanation you’ll need (besides simple 5V/2A+ charger):
a. one USB-A male to USB-C male cable from 5V charger to StayGo “pass-through USB-C port”, and
b. one USB-C male to USB-A male data transfer (5Gbps) cable from StayGo “USB-C port to computer” connected to the one of your laptop USB-A 3.0 ports (my preference is to avoid USB-C port on laptop, but who knows, I’m not an engineer).
Device like Librem 5 you should connect to StayGo “USB-A + Power” port (only BC 1.2 charging port that I see there). Of course, when you find adequate 5V/2A+ (only) charger you should proof if Librem 5 charges well in offline mode (while not connected to the laptop).
As well, perhaps you would like to read out your connected StayGo usb.ids, with lsusb as described within this post, first one (for your further orientation).
P.S. Please play around with hub that you currently own, I just talk here (and have no talent to sell something) and therefore rethink your next step carefully (don’t take my advice here for granted). But hey, there is slight chance that StayGo finds his way to communicate well (better) with your Librem 13v4 (it’s your turn now).