The 3rd Party section of the software center is deprecated. To quote its github readme:
Third Party Apps (DEPRECATED)
Note: This repo will not accept NEW packages as we are replacing the majority of them in Solus with a modern solution like flatpak. After we have flatpak integrated in the Software Center we will begin forceful deprecation of this repository.
Source: https://github.com/getsolus/3rd-party/
For applications to enter the actual repository it must have a license that allows third party distribution.
EDIT:
Because people often misunderstand this, no we are not going full universal package only or anything like that. It is specifically for the 3rd party section of the software center which contains software we can not legally distribute in our repository due several projects having a license preventing third party distribution.
Software in this section is not distributed by us. It simply contains a build recipe that your system uses in real time to repackage these programs for Solus.