Why do you need to tell the TG series cameras that you are using a FCON T01 or a FCON T02 Lens. What does the camera do or not do if you don't ?

I got the answer from AI, did not verify it, but makes a lot of sense, hope it helps:

You need to tell your Olympus/OM System TG-series camera (TG-6, TG-7, etc.) that you're using an **FCON-T01** or **FCON-T02** fisheye converter lens in the menu because the camera uses this setting to apply the correct **optical corrections and zoom behavior** for that specific lens.

### Key point from Olympus documentation:

> "When using the FCON-T02, change to settings appropriate for shooting with the converter: In Live Control's **Accessory Settings → Converter Name (Conversion Lens)**, select **[FCON-T02]**" [2]

### What happens if you don't set it:

The biggest practical issue is **vignetting** (dark/black corners around your image) because the camera doesn't apply the distortion/vignetting correction specific to that fisheye lens [3]. You'll still get the fisheye effect mechanically, but the image quality degrades significantly at the edges.

And probably for the same reasons I explain here.

The electronic IBIS must know the real lens FOV to electronically compensate your movements.