Well, the issue has been fixed. I’ll post the solution in case anyone else runs into the same problem.
The fix was to delete files leftover after uninstalling the game
I was already deleting leftover files located;
C:\Users\me\Documents\Command & Conquer 3 Kane’s Wrath
C:\Users\me\Saved Games\Command & Conquer 3 Kanes Wrath
C:\Users\me\AppData\Roaming\Command & Conquer 3 Kane’s Wrath

But there was a fourth set located here;
C:\Program Files (x86)\Steam\steamapps\common\Command and Conquer 3 – Kane’s Wrath

>Did you install the 4k mod aswel?
Yes, it seems I neglected to mention that. For my first install, I had the 4k pack. I did not reinstall it while I was troubleshooting

Anyways, before I fixed it the results were;
Default Kane’s Wrath Skirmish – Works
C&C Online Skirmish – Works
C&C Online + R22F Map packs – Game no longer launches

After the fix C&C Online, the R22 map packs, and the 4k mod are all installed together and working without any issue