The issue of printers failing to recognize the computer after the update is common and can attribute to the fact that the update might have deleted certain drivers required for proper functioning of the printer. I will discuss a few troubleshooting techniques hopefully this would help. Follow the instructions carefully:
Add your Printer to your computer
This is the basic step and you need to add your printer to your computer as the default printer. Go to, "Start" > "Control Panel" > "Add a Printer or Network device". Now switch on your printer and let your computer search for it. Once detected, click on your printer name and then follow the on-screen instructions to complete the procedure.
Make sure your printer and computer are on the same network
At times when your printer and computer are on two different networks, chances are that your computer would not be able to find it. So make sure both your computer and printer are on the same network.
Update the driver
At times when you update the operating system of your computer, it automatically deletes certain drivers which it feels are not necessary. This could be one of the reasons why your computer is not able to find your printer. So go to your printer's official website and then search it via model number. Now go to the "Downloads & Update" section of your product and download all available drivers for your printer in its latest version and then install it on your computer.
Reset your Printer
If any of the above-mentioned technique did not help you resolve the issue, you can reset your printer to factory settings. This will ensure that any issues arising due to change in settings of the printer get eliminated. So make sure to reset your printer and then trying the first 3 steps again and see if it works.
Hopefully, these steps helped you resolve the issue. In case you have any doubt regarding the steps kindly revert back to your query.