apt-get update "The following signatures were invalid..."

[grump_fiddle_reinstall]

Try
sudo apt-get dist-upgrade

[LibrePhoneUser]

Can't update here as well. I can't install curl (I get 404  Not found) so I tried using wget above but it makes no difference. 

404 Not Found errors on a new install of Mobian are caused by trying to download from an automatically-selected Debian mirror that is incomplete. If you manually choose a Debian mirror (one that is actively maintained) and enter it in /etc/apt/sources.list, you won’t have 404 Not Found errors any more.

[mthwbrwn]

This checks out -  you can find a suitable mirror here: https://www.debian.org/mirror/list

The only thing I would add is that you do need to comment out the current listed archive since there seems to be some issue currently with that server.
This worked for me.  You should be able to select whatever mirror is close.

/etc/apt/sources.list
#deb http://deb.debian.org/debian bookworm main
deb http://debian.csail.mit.edu/debian bookworm main




404 Not Found errors on a new install of Mobian are caused by trying to download from an automatically-selected Debian mirror that is incomplete. If you manually choose a Debian mirror (one that is actively maintained) and enter it in /etc/apt/sources.list, you won’t have 404 Not Found errors any more.

[Eugo]

I just read somewhere on mobian's site that apt-get gets you less than just apt, and that apt upgrade is a bit conservative, it won't drop unused stuff, won't install what already wasn't there, that apt dist-upgrade will. Also, it said that the apt-get dist-upgrade combination is most likely to fail a lot.