Believe it or not, the setup you see in the above picture works. The Fire TV Stick 2 supports OTG USB cables out of the box without needing to root the device or change any configuration settings.
Fire TV 3 supports USB Peripherals via OTG Cable — Including USB Drives, Keyboards, Mice, FLIRC, Ethernet, Hubs, etc…
Fire TV Stick 4K Max (2nd Gen, 2023) Review
External Storage Support Explained Across All Fire TV Models — Fire TV Stick 4K vs 4K Max differences and more
This 4-Port USB Switch is an excellent choice to share 4 USB devices between two computers. It's ideal for sharing a printer or scanner in a small office environment. It's also great for use at home if you have multiple PCs or Macs.
UGREEN USB Switch Selector 2 Computers Sharing 4 USB Devices USB 2.0 Peripheral Switcher Box Hub for Mouse Keyboard Scanner Printer Pcs with
2 in 1 USB Power Adapter and OTG Cable for Fire TV Stick,2nd Generation USB Power Cable Cord for Fire Stick.TV's USB port to power streaming devices(Eliminates The AC Outlet and Power Cord) : Electronics
21 Fire TV Tips for Streaming Fans
2 in 1 Micro USB OTG Adapter with Power for Fire Stick/Host Devices etc - 2 Pack 20cm/7.87in Dropshipping
This all-in-one adapter is the easiest way to add Ethernet to the Fire TV Stick
Fire TV Stick with Alexa Voice Remote (includes TV controls), Dolby Atmos audio - 2020 release