Why the app body battery doesn t work on fenix 5 plus ?

The Instinct also got Body Battery in a recent update. So maybe there's still hope for the 5 Plus series.

Is there any update to this?

Garmin wants you to buy a new watch, so they will not upgrade "old" watches, although the hardware can perform that (probably since the Fenix 1). Sustainability is obviously not a target for Garmin. You have to decide if you want such opinions. For me GPS-accuracy has a very high priority, so I will definitely not upgrade to one of the Garmin watches with the new Sony GPS chip. As an experienced runner accuracy has a much higher importance for me than estimated  stuff like VO2 max, Pace Pro, Body battery etc.

Features like this are pretty gimmicky as they rely on an optical heart rate sensor (which are not very accurate), and attempts to measure HRV via the optical heart rate sensor (also inaccurate, and technically hard to do)

IMHO you are better off monitoring your resting heart rate trends - the heart rate sensor in the Fenix 5 Plus is VERY good for measuring resting heart rate, and is within 1 BPM of both my Wahoo Tickr and Polar H10 heart rate belts. Just monitor those trends.

The new watches have poor GPS accuracy and have traded off power consumption for accuracy - I think for most folks the more accurate GPS of the Fenix 5 series is more useful than a dubious metric based off optical heart rate technology.