GPS satellites don’t know where your phone is. They tell your phone where they are, and it derives where it is from the position of the satellites.
It’s the cell towers that actually track your phone. You can deal with this by putting it into airplane mode (provided that actually shuts off the modem) or using a hardware kill switch to shut the modem off (provided your phone has that).
So if you don’t want to take your phone with you, there are lots of products you can get for your car that’ll let you navigate without being tracked.
Unless your car has a cellular modem in it, which most new ones should be assumed to have.
As for the things introduced on account of SARS-COV-2, there isn’t a guaranteed way to avoid that. Checkpoints that need a QR code to let you past (AKA “vaccine passports”) aren’t going to be something you can avoid unless you can convince your government to ban them. They can be as simple as another phone or tablet. Saying you don’t have a phone won’t work as an excuse, as the plan is to have the checkpoints accept QR codes printed on paper as well. You can avoid the contact tracing by using a Linux phone or a phone with an AOSP custom ROM.
But for my own purposes, I would like a device with a color e-ink display that can read documents, store maps, and mark waypoints (ideally, draw on the map too), and whose self and power supply take up less space or weigh less than a book and some maps.