Thank you for posting your query on this forum, it's a great place to find answers.
I reviewed your post and I understand that you are having issues updating the sprocket firmware.
Don’t worry, I assure you I will try my best to get this sorted.
I did some research and found that there is no firmware update available as of now for the HP Sprocket printers. If there is any firmware update released then you may update it via the sprocket app. Please refer to "Update the printer firmware" mentioned under "What if the printer does not print?" from the below link.
To simply say thanks, please click the "Thumbs Up" button to give me a Kudos to appreciate my efforts to help. If this helps, please mark this as “Accepted Solution” as it will help several others with the same issue to get it resolved without hassles.