How can I upgrade my "obsolete" Pixel to a current/secure version of Android?
You could install LineageOS for Pixel 1 (sailfish).
However as Google does not provide updated kernels (and drivers) the updates will only affect problems in the Android system itself.
The disadvantage is that the whole system is no longer genuine regarding Android SafetyNet check so that certain apps (especially payment/banking apps) may refuse to work.