Finally after weeks of banging my head against the wall I’ve found that this issue was already solved over a year ago but no one bothered to update the docs like they said they would. See this post by mod @Bucking_Horn which contains new properly working nftables rules to enable NAT.
The other smaller issue of enabling IP forwarding comes from RaspiOS no longer using /etc/sysctl.conf. You have to create the specified file and add the rules or just add them to the existing file /etc/sysctl.d/98-rpi.conf and then load that file with sudo sysctl -p /path/to/file. Hopefully someone can update the doc with these instructions as well.