I wouldn’t say it’s phony, but it’s not real time. The only real time reading I know of is from a Mac program called coconutBattery.
https://www.coconut-flavour.com/coconutbattery/
It provides what the developer calls a “defensive” reading which varies at different readingS but overall follows a trend. It also provides the cycle count recorded on the onboard battery diagnostics, and as far as I know the only other way to read the cycle count is through an official Apple diagnostic. I got that with my battery replacement service, and when it was complete the Apple Store employee saw stream of data on his iPad Mini and then authorized the battery replacement.
My last iOS Battery Health reading is 99%. I’m kind of skeptical, but coconutBattery last said it was 98.0% at about 176 cycles. For whatever reason (and I’ve done nothing special) his battery isn’t losing much capacity.
Can’t be too sure what’s the issue with your battery where it’s stuck at 84%, but you could have replaced it during the $29 promotion. My wife got a new battery for her 6s Plus, and it was showing Battery Health at 83%. You could still get it replaced now, but it’s $49.