7-zip does not support JPA files, nor does it support split ZIP archives (what Akeeba Backup and Akeeba Solo creates). You cannot use it to view files in archive files taken by Akeeba Backup.
It sounds like you made this all up.
Akeeba Backup has been used to back up and restore sites hundreds of millions of times since 2006.
The very fact that we are having this conversation on this site —developed on a local server, backed up by Akeeba Backup for Joomla!, and deployed on the live server using Kickstart— is the living proof that Akeeba Backup works fine and includes all files and database data. We have done that several times over the years, across all major Joomla versions. We use our own software. Heck, I first wrote JoomlaPack —that's what Akeeba Backup was called before version 3— exactly because I needed a way to transfer whole sites between local and live servers, and back up the sites which were on live servers.
Hundreds of Joomla! templates are delivered as JPA or ZIP files created with Akeeba Backup as a sort of “quick start” site with the corresponding template preinstalled. If what you allege was true, these couldn't exist. They fact they do exist for well over a decade and the fact they all use Akeeba Backup for this purpose proves that Akeeba Backup does back everything up.
Finally, the archive format does not have any effect on what is being backed up. Which files get backed up depends entirely on their permissions and your filters. Filters are defined per backup profile. If something is unreadable, Akeeba Backup will issue a warning about it.
In case that you only made up the part about 7-zip, your problem is a self-inflicted one. You are probably backing up the wrong site (each Akeeba Solo profile can be configured to back up a different site), or you have unreadable files (it's totally possible for a file to be web accessible and unreadable by PHP at the same time) but ignored the warnings. Of course, in the latter case both JPA and ZIP files would have the same problem. Or maybe you misconfigured the filters in your backup profiles.
Nicholas K. Dionysopoulos
Lead Developer and Director
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