The problem seems to have resolved with no additional action from my side. I would still consider this a bug.

The next day, the problem reappeared. Installing packages is not possible today, but was for a short time (yesterday). Before yesterday, installing wasn't possible either.

This is indeed a problem with Discover, as updating using Muon or running sudo apt update && sudo apt upgrade works fine.

Yes, that makes sense. Thanks for reporting, will look into it.

*** This bug has been marked as a duplicate of bug 410843 ***

I have the same error.

Operating System: KDE neon 5.19
KDE Plasma Version: 5.19.5
KDE Frameworks Version: 5.74.0
Qt Version: 5.15.0
Kernel Version: 5.4.0-48-generic

A solution to this problem has been posted here: https://forum.kde.org/viewtopic.php?f=309&t=161739#p430783

The work-around above is not a fix or a solution, it's a dirty workaround,

New KDE users would expect Discover to behave like other applications: act correctly on current KDE settings.

Discover should behave correctly: i.e. check KDE proxy settings, 
not "assume" old outdated incorrect disabled proxy details. My 2c opinion.

I see this bug, too.  It's somewhat of a pest because notifications show frequently on the desktop letting you know that connecting to the proxy failed.

I've just switched to KDE.
This proxy problem is really annoying when you use your pc in a professional environment.
For my part I found that :
1 / the proxy settings in system configuration tools are not saved
2 / if I configure kioslaverc manually it works except for packagekit (except the first time),
3 / at the first configuration of kioslaverc (or apt.conf??) the proxy settings for packagekit are saved in transactions.db but, if you need to use another network without proxy, there is no way back. The only solution is to delete the transactions.db file (/var/lib/PackageKit/transactions.db).
This is a very annoying problem.
It is a concern especially the 1 exists under Neon and on kubuntu 20.04, so for this one it is certainly related to KDE and not to package kit.

Hello!
I have th same problem:
SUMMARY
Discover is trying to use proxy, which was removed from the system

STEPS TO REPRODUCE
1. Launch Discover
2. Press Update all
3. 

OBSERVED RESULT
Не удалось загрузить пакет.:

E: http://ftp.linux.org.tr/ubuntu jammy-updates/main amd64 ubuntu-pro-client-l10n amd64 31.2.2~22.04 is not (yet) available (407 Proxy Authentication Required [IP: 176.222.59.2 59704]) E: http://ftp.linux.org.tr/ubuntu jammy-updates/main amd64 ubuntu-pro-client amd64 31.2.2~22.04 is not (yet) available (407 Proxy Authentication Required [IP: 176.222.59.2 59704]) E: http://ftp.linux.org.tr/ubuntu jammy-updates/main amd64 openssh-client amd64 1:8.9p1-3ubuntu0.7 is not (yet) available (407 Proxy Authentication Required [IP: 176.222.59.2 59704]) E: http://ftp.linux.org.tr/ubuntu jammy-updates/main amd64 ubuntu-advantage-tools all 31.2.2~22.04 is not (yet) available (407 Proxy Authentication Required [IP: 176.222.59.2 59704]) E: http://ftp.linux.org.tr/ubuntu jammy-updates/restricted amd64 firmware-sof-signed all 2.0-1ubuntu4.7 is not (yet) available (407 Proxy Authentication Required [IP: 176.222.59.2 59704]) E: https://dl.google.com/linux/chrome/deb stable/main amd64 google-chrome-stable amd64 124.0.6367.60-1 is not (yet) available (Invalid response from proxy: HTTP/1.0 407 Proxy Authentication Required Proxy-Authenticate: Basic realm="proxy" Connection: close Content-type: text/html; charset=utf-8 [IP: 176.222.59.2 59704]) 

EXPECTED RESULT
Sucsessfull update

SOFTWARE/OS VERSIONS
Windows: 
macOS: 
Linux/KDE Plasma: 5.24.7
(available in About /System)
KDE Plasma Version: 5.24.7
KDE Frameworks Version: 5.92.0
Qt Version: 5.15.3