Upgrade from 16.04 to 18.04 broke apt

How I got to where I am now:

I started the upgrade from Ubuntu GNOME 16.04 to 18.04.

Everything went fine until I was asked to reboot.

It got stuck at displaying /dev/sdb6: clean 723689/3620864 files, 11918552/14478592 blocks.
I switched into tty4.
There it said

Welcome to Ubuntu 18.04 LTS....
...
...
*** System restart required ***...
...

So following some other Ask Ubuntu answers I tried

sudo dpkg --configure -a

which didn't work. Then I did

sudo dpkg --configure -a  --force-depends

After that, I did

sudo apt --fix-broken 

Then I rebooted. It booted correctly into Ubuntu GNOME.
I did apt update

The actual problem:

apt seems to be broken:
When I do apt upgrade it returns:

Some package could not be installed. This may mean
that you have requested an impossible situatio

or if you are using the unstable distribution that some required
packages have not been created or been moved out of Incoming.
The following information may help to resolve the situation:
The following packages have unmet dependencies:
  python3-aptdaemon.pkcompat : Conflicts: packagekit
                               Conflicts: packagekit:i386
E: Broken packages

How could I fix that?

If you need more information, feel free to ask.

(Also, if this is somehow important: DNS wasn't working until I manually added 8.8.8.8 to resolv.conf)