Solved. I’ll do my best to document this here, anyone finding this feel free to reach out!
I deleted a KASA 100 series bulb from my HA server whilst troubleshooting something. It then failed to show up, even when I factory reset it and added it to the TP Link Kasa app with a new name.
Upon targeting the IP of the bulb in question (With the Kasa integration setup), I recieved the “Device already configured” message. I assumed (correctly) this meant orphaned registry entries that were no longer accessible from the UI.
So, I installed the community SSH Add-On, stopped my HA server core while leaving the HA OS itself running, and accessed the filesystem of my server with WinSCP. I then searched for the MAC address of the orphaned bulb in the core.config_entries, core.device_registry, and core.enities_registry JSON files. I deleted the entry blocks for these carefully, making sure the syntax before and after was left intact.
You mileage may vary, but this worked for me and I was able to add and use the device again!