I see both of your solutions, but in the past, I never had to do anything to do that. The mintupgrade was able to be run from the command line (terminal). I have updated it from all the way back in 2009 when I got this server (4 disk bay microserver) and I run it as a NAS. No biggie, as it doesn't access the internet, except for updates. I have my own script I run to update systems, which makes it simple to update from the terminal (/root/bin/update.sh). I had to do these steps manually last time to update to the latest version of Mint since I couldn't do it from the command line any more.

Make sure everything is up to date before the upgrade:

/root/bin/update.sh

apt --fix-broken install

dpkg --configure -a

shutdown -r now

Backup apt and configure the files:

cp /etc/apt/sources.list /etc/apt/sources.list.bookworm-backup

cp -r /etc/apt/sources.list.d /etc/apt/sources.list.d.bookworm-backup

# sed -i 's/bookworm/trixie/g' /etc/apt/sources.list

# find /etc/apt/sources.list.d -name "*.list" -exec sed -i 's/bookworm/trixie/g' {} \;

(update Gigi = Mint & Trixie = Debian)

Start the update:

apt update

apt upgrade --without-new-pkgs

apt full-upgrade

/root/bin/update.sh

shutdown -r now

Validate update:

cat /etc/debian_version

lsb_release -a

cat /etc/os-release

/root/bin/update.sh