A rooted Pixel should be regularly updated to keep it secure (and stifle the annoying update nag notification). Once you've unlocked the bootloader, over-the-air (OTA) updates can't be installed by the operating system due to failing security checks. It needs to be done manually. This can happen without erasing the phone, but you'll need to re-root and possibly apply SuperSU and SuHide again. You should always back up your files anyway in case of problems.
This guide is based on a very helpful XDA article, but attempts to fill in procedural holes and improve clarity for my own benefit. It will be improved as needed. I intend to own and operate my (awesome, but very expensive) Pixel for at least 3 years. The root procedure itself is outside the scope of this article.
Please do not request support in the comments other than to ask for clarification of these instructions. I am a software engineer, but I am not an Android developer and have limited knowledge of the Android OS. Please do share your tips and suggestions for improvement of this article.
Also, it is assumed that you will read carefully and follow all advice, as appropriate in your particular case.
Before you begin, decide whether backing up specific files or creating a full, restorable system image is important to you. I'm not your mother and I won't yell in caps about this. Be your own buffalo and do it or don't. I use Titanium Backup Pro and other means to do so.
Note: We'll be wiping the internal storage area of the phone. This is what you see when you browse the phone on your computer. Back up any files and folders that you need from there. It potentially contains photos and videos, app data, backups, etc.