I have extracted the sw-file from the update image, but can't seem to find out how to mount it, or understand the structure in order to extract files.

I have searched here (and on google) without finding anything.

Anyone know the format?
There was a python script called pbfwsplit.pl floating around the net that could be used to extract the pieces inside of the unzipped file. However, last time I tried it a few years ago, it wouldn't work on the latest firmware updates anymore. You can probably still find it to see how the unpacking was done then, just to see how much reverse engineering would be required to update the script.
Thank you. Found the script but didn't work as you said. Also found an old description of the format of the image. (Both from 2011.)

Oh well...

What I wanted to try is to see if a binary for the Inkpad 2 would run on Inkpad 3. Do you know if that is probable?

(If anyone has an Inkpad 2 here and would like to help, please send me a mess.)
You can check the SDK available for each to see if the libraries are the same on both devices. If so, I think the binaries would be able to start up on both systems. However, if some feature depends on the exact system configuration, and that has changed between systems, then the binaries may not run properly. I think all you can do is try and see.
Actually, the perl script still works fine, but the new SWUPDATE.BIN is gzipped, so you need to first decompress it for a script to be able to extract firmware.
Yes, it works! Thanks! I wish I had more karma to give you.
Just like rkomar said, it depends on the libs functionality it's implementing. Usually things should work from one device to another but sometimes there are breaking changes introduced in the libs and stuff stops working as expected.
Thanks, great news that the script works.

Now, if I just could remember what program it was I wanted to test...
I use the tools described at https://www.synacktiv.com/posts/hardware/e-ink-maiden-bring-your-reader-to-the-reverser.html
Thank you! Glad I could help.

Interesting read, thanks!