So the problem is with the sources.list file being used. Ultimately it links to a keyring, which doesn't contain key AA16FCBCA621E701.
In my case this was the file /etc/apt/sources.list.d/hashicorp.list
deb [arch=amd64 signed-by=/usr/share/keyrings/terraform-archive-keyring.gpg] https://apt.releases.hashicorp.com jammy main
The above notes (thank you MacroMan), led me to this (which creates a new, valid hashicorp-archive-keyring.gpg, his original instructions don't work unless you're running as su - root, which I never do)
curl https://apt.releases.hashicorp.com/gpg | gpg --dearmor | sudo tee /usr/share/keyrings/hashicorp-archive-keyring.gpg
With the new keyring, edit the above file to replace terraform-archive-keyring.gpg with hashicorp-archive-keyring.gpg and sudo apt-get update should run without errors.
Alternatively (I didn't run this, but someone might find it useful, as it recreates the sources.list using sudo tee, so doesnt need to be run as root, as > does)
echo "deb [signed-by=/usr/share/keyrings/hashicorp-archive-keyring.gpg] https://apt.releases.hashicorp.com $(lsb_release -cs) main" | sudo tee etc/apt/sources.list.d/hashicorp.list