There seems to be a few issues raised. The following is how I see it.
@Alexzee wrote
The "fresh" installation of debian I take to be trixie. In that case you can find the .deb file in the output of the following command:
Code:
$ apt-get download --print-uris firefox-esr | awk -F"'" '{print $2}'
http://ftp.au.debian.org/debian/pool/main/f/firefox-esr/firefox-esr_128.14.0esr-1_amd64.deb
Note that the output is from the repo that is used in the sources list on this machine, thus, the repo from which the output derives will depend on your sources.
Once the full pathname to the .deb file is known it can be downloaded with wget or curl, and then installed with apt. It is apt that will bring in dependencies if any, so apt is better than dpkg.
HOWEVER, note that this is not the normal means of installation in debian. It's inefficient "double dealing" to download the .deb file and then install it when apt can install it with a single command:
apt install <pkg>.
It's possible to install in this "double dealing" way, but inefficient and not really done in debian for packages that exist in the repository. It's a different matter for external packages not in debian repos which apt cannot access through sources lists. In that case, one can work with the downloaded non-official-debian .deb file.
Another major point to note I think is this: if one is using stable trixie, the firefox-esr installation won't change unless there's a security update or a bug fix. That's the way with stable releases. That means that "updating to the latest firefox-esr" may not get the latest firefox-esr that is available from the mozilla repos. If, by chance you want to get a later, or the latest firefox-esr, then the recommended way from mozilla for debian is to use their repos which
@craigevil linked to, and configure the repos on your machine as outlined in the link in post #3 for trixie.
Personally, I no longer bother with firefox-esr because the latest firefox browser is superior software in many respects which can be researched in the changelogs and the release notes.
Since you mentioned doing things "by hand", if, by chance you wish to install the latest firefox by hand, that can be done by downloading the latest firefox tarball (not the .deb file), installing it in the /home/$USER directory somewhere and running it. It will not conflict with an existing firefox-esr, rather it creates it's own configs in the /home directory under /home/$USER/.mozilla. If you are interested in this manual option just ask and I can provide the means of doing it in great detail