This is all based on my FZ952, which I believe is similar to your FZ800. The FZ OLED's have separate settings for HDR and SDR, so your SDR calibration won't be lost when you calibrate HDR. However, some settings are shared between HDR and SDR, most notably the BRIGHTNESS setting, so don't adjust BRIGHTNESS in SDR to fix black levels, as it messes up the HDR setting. You'll need to adjust black levels using the 2.5 and 5 gamma settings.
Make sure you're using the correct meter profile. Don't use the OLED profile, use RAW. And use an accurate pattern generator. The FZ TV's are pretty accurately calibrated out-of-the-box, so there's a real danger of making things worse with an inaccurate pattern generator or meter.