Accept no substitutes.
RTCs for the RasPi that don't use the GPIO pins but a USB jack are apparently a thing. Battery backed.
- https://shop.sb-components.co.uk/products/usb-rtc-for-raspberry-pi-1
- https://thepihut.com/products/usb-real-time-clock-rtc-for-raspberry-pi
Software for using those RTCs: https://github.com/sbcshop/USB-RTC