Same problem here with a 6s. Had 94% battery health prior to upgrade, now it's a 89%. Have spent hours, HOURS on the phone with Apple Support and a solid 90 minutes in the store. Absolutely a waste of time. They have nothing to offer and they refuse to admit it is a problem. Support has now done remote diagnostics on my phone three separate times and keep swearing they're working with their development teams to find a resolution. A complete lie, all of it.
I have an Apple branded battery-phone case that is now flaky. If you put the phone in the case while the phone is powered on it does not recognize the battery case. If you bounce the phone (power cycle) it'll recognize the case and start charging. However as soon as you remove it and replace it, even for a second, it won't charge again. Even worse is that my battery was at 20% when I put it in the fully charged case. The case went down to 40% and the phone only managed to go up to 48%. So it took 60% of the case's capacity to charge the phone 28%? I know the battery case's capacity is about 80% of the phone, but this is utter garbage.
Every time I'm on the phone with Apple Support I call out the battery percentage as it drops. I also take screen captures at the beginning, during, and at the end of the call. During a 40 minute phone call the battery went from 28% to 12%. Around the time I announced 18% the support person was laughing.
None of it matters though. They have no solutions. Don't bother taking it to the store, they won't be helpful and they'll just tell you to call Apple Support. The first thing they'll ask is if you did an upgrade and include your old data. They'll want you to wipe the phone and start from scratch, meaning having to download all of your apps again, set them all up, sign in to them, etc. Don't. Just flat out refuse to. It's a waste of your time and energy. I did this on my backup 6s. Complete wipe, went into DFU and loaded the IPSW manually, then downloaded all of my apps. Did not sign into a single app or touch any of Apple's default settings. That phone sitting on a desk dropped 7% in an hour, doing nothing. By the next morning it was down to 65%, with cellular, wi-fi, and bluetooth all turned off (not disabled, but actually off).
This is Apple forcing planned obsolescence. I like my 6s, it's the size I like and I like the fingerprint reader with 3D touch. No way I'm going to spend hundreds of dollars to keep those features with an 8. Cause you know it'll be in the same situation as the SE's and 6's are. Even though the chips are "64-bit" I don't think the OS is optimized to run on them correctly. Why else would your battery drop 5% just opening something like Safari?
Just to demonstrate how flaky, unstable, and unreliable iOS 13.1.2 is on a 6s I fully charged my phone and put it in Airplane mode. It sat for a week and the battery went down to 50%. I enabled wi-fi and bluetooth (still in Airplane mode), it "thought" for about five seconds then shut off. When I went to start it back up I got the "plug in charger" graphic. I plugged it in, and when it auto-turned on the battery was at 10% not two minutes later. In five minutes it was up to 25%. I power cycled the phone again and it jumped to 50%. Got screen caps of all of it. Not that giving Apple hard evidence they can't refute will do the slightest bit of good.
Seriously, we are all the [proud] owners of expensive paperweights. Go ahead an thank Apple for it. And good luck reaching anyone at Apple that'll care to help. Notice how there is only one number to call for any kind of issue? Not even a number or a way to reach Customer Relations. They just shuffle you to a Support person who won't offer any kind of consolation or compensation.
If you do happen to work up to a Senior Tech Analyst make sure to document everything. I got one that told me they'd call me back in 48 hours. When I didn't hear anything I started to email them with the reference # they gave me. The person called me back three days later stating he wasn't at work those two days and he told me he worked four 10 hour days. Another load of crap. If you told me that you wouldn't be at work, then why did you also tell me you'd call me back on the day you'd be off? They lie through their teeth. Don't let them off the hook when they say "they'll let you know when they hear something". Get a number, get an exact date. Have them proclaim something definitive, as it's being recorded, and they'll be on record with it. Even getting them to do that is a challenge.
I really do wish the best of luck to all of you. But having now dealt with this for the third time (iOS 11, 12, and now 13) I can tell you from experience there is nothing Apple can or will do to fix your battery problem. Nothing.