Update: 03.04.2023
As of today Django 4.2 is released.
One change is support for newer GDAL version. See list: here
OSGeo4W does now also distribute a new gdal305.dll
library. Therefore I gave it a shot & installed a fresh OSGeo4W with GoeDjango 4.2.
This worked out of the box. My recommendation at this point, upgrade as soon as possible to Django 4.2 and update you OSGeo4W. With this, none of the hacks below are necessary any more.
Old Comment (Prior 03.04.2023):
I ran into this problem too, since I updated my old GEO Django Setup today.
You may use a Docker Image as suggested by the others, but I prefere a native solution, since I don't want to spin up Docker every time I start coding.
Your solution is in the brackets: (or one of its dependencies)
You may look up the transitive dependendencies from gdal304.dll
. There are several tools for this (see here). I'm using here now the Git integrated MinGW - Shell that has ldd
installed. This should be the case for any (newer) Git installation on Windows.

As you can see, some dependencies are already fullfilled from your operating system. Others that are missing, have to be fullfilled from OSGeo4W. If you compare this with your bin
directory from OSGeo4W you will see the Problem:

Sadly a simple "renaming" does not the trick. I was lucky and had not yet deleted my old OSGeo4W version. In the old files I then found the necessary DLL.

So, long story short: You need the jpeg.dll
file.
There are sites like "windll.com" or "dll-files.com", but I would not recommend using them. I don't trust these sites. You may install something like "MSYS2", "Cygwin" or even "MVSC", install the "libjpeg-turbo" library and then finally copy & paste the necessary DLL file.
This is also suggested on the official Site for libjpeg-turbo: https://libjpeg-turbo.org/Documentation/OfficialBinaries
But this seems like a lot of work for someone who just want to have the DLL file, but then again: Never download a library blindly from the Internet and load it into your application. These libraries could do anthing!