USB-A is limited to an absolute maximum of 5V 2A (though more typically 5V 0.5A) - unless you're using a proprietary rapid-charging protocol (like Qualcomm's QuickCharge), which Pixel phones have never supported.
The only rapid charging which Pixel's support is the Power Delivery spec that goes along with USB-C.
You can probably slowly charge your Pixel 6 off of the USB-A charger if the phone is powered off but, like Jim mentioned, that charger isn't going to provide the phone with enough power to charge the battery while the phone is turned on. I imagine the battery would drain at about the same rate it was charging and that is TERRIBLE for a battery's long-term health.
I know that having to buy new modern accessories for your new phone kind of sucks, but do yourself a favor and pick up a couple of PD-capable chargers. They can be had for pretty cheap, and you'll be glad to have them.
Cheers,
John