How can I view the content of a backup of the dconf database file?

To view the content of that file you could rename it - e.g. test - place it under ~/.config/dconf/ and then have dconf read/dump the settings from that file.
By default, dconf reads the user-db found in $XDG_CONFIG_HOME/dconf/:

A "user-db" line specifies a user database.
These databases are found in $XDG_CONFIG_HOME/dconf/. The name of the file to open in that directory is exactly as it is written in the profile. This file is expected to be in the binary dconf database format. Note that XDG_CONFIG_HOME cannot be set/modified per terminal or session, because then the writer and reader would be working on different DBs (the writer is started by DBus and cannot see that variable).

As a result, you would need a custom profile that points to that particular db file - e.g. user-db:test and then instruct dconf to dump the data (using the custom profile) via the DCONF_PROFILE environment variable:

cd
cp /path_to_backup_dconf/user ~/.config/dconf/test
printf %s\\n "user-db:test" > db_profile
DCONF_PROFILE=~/db_profile dconf dump / > old_settings

The result is a file (old_settings) containing the settings from your backed up dconf file, e.g.:

[org/gnome/desktop/interface]
font-name='DejaVu Sans Oblique 10'
document-font-name='DejaVu Sans Oblique 10'
gtk-im-module='gtk-im-context-simple'
clock-show-seconds=true
icon-theme='HighContrast'
monospace-font-name='DejaVu Sans Mono Oblique 10'

[org/gnome/desktop/input-sources]
sources=@a(ss) []
xkb-options=@as []

[org/gnome/desktop/wm/preferences]
num-workspaces=4
titlebar-font='DejaVu Sans Bold Oblique 10'

.......

You could then remove those files:

rm -f ~/db_profile ~/.config/dconf/test

and load the old settings into the current database:

dconf load / < old_settings

---

If you want to dump only specific settings just provide the path:

DCONF_PROFILE=~/db_profile dconf dump /org/gnome/desktop/wm/preferences/
[/]
num-workspaces=4
titlebar-font='DejaVu Sans Bold Oblique 10'

but note that for each path you should have a different file and when you load it you should specify the path accordingly:

dconf load /org/gnome/desktop/wm/preferences/ < old_wm_settings

---

Also note that, due to upstream changes, older dconf databases might contain paths, keys and values that are invalid in newer versions so full compatibility between db-files created by different versions of dconf isn't always guaranteed. In that case, you would have to inspect the resulting old_settings file and manually remove or edit the entries that are invalid before loading it into your current database.