Minor note, it looks like the Amazon listing might be a bit off on that. Looking at the Jackery store itself, instead of two 3.4A ports, it's 1A+2.4A ports. If the Switch doesn't charge off one port just try the other.
If the Ethernet adapters work fine when docked but not with the extension cable...it's probably the extension cable (or perhaps the seating). Do you know the spec of the cable (USB 2.0, 3.0, 3.1*?), and what length is it? If it's a longer cable you might want to try a shorter one. I'd guess it's just a signal degradation thing.
*Technically 3.0 got semi rebranded to "3.1 gen 1" once 3.1 came out, which itself became "3.1 gen 2". Or "Superspeed" vs "Superspeed+", or 5gbps vs 10gbps. I'd be kinda surprised if the Switch used 10gbps USB cause it isn't necessary for what it has now, but who knows.