Did you read the post I linked where I explain with an example how the FCC value fluctuates even with good healthy Apple Lithium batteries? The FCC value is used in the computation of the macOS Maximum Capacity value. I'm not sure how often the Maximum Capacity value is recalculated. I personally would trust the information reported by Coconut Battery since I believe it is updated more regularly from the little bit I've referenced the Coconut Battery app (I utilize the built-in macOS command line utilities to access the battery information so I can monitor the battery information in real time which Coconut Battery does not display as often although it may recalculate the battery health more often. In my own personal experience....macOS does not do a very good job in this area, nor in most areas related to assessing & reporting on system hardware health (I've worked with Apple hardware for over 20 years and have developed methods for assessing hardware health that macOS & the Apple Diagnostics never catch or alert).
When supporting thousands of Apple laptops in my organization.....it is a priority for me to best evaluate hardware health in order to keep our Apple laptops running as smoothly as possible. I have never met anyone else who has ever evaluated Apple hardware like this...even online...certainly not Apple or AASPs which only rely on the Apple Diagnostics.
Did you even notice that Coconut Battery is reporting the FCC value above the Design Capacity? And that the FCC value went up as well as down by several percent? This is common on new batteries, but users would never realize it because the macOS GUI doesn't normally show the Design Capacity and never previously shown the Maximum Capacity value to users before so people don't understand how these batteries operate.
4563 Design Capacity
FCC Date Calculated Rounded (aka Maximum Capacity value)
4599 6/12 100.79% 101%
4639 6/14 101.67% 102% increased by 1% from 6/12
4589 6/15 100.57% 101% decreased by 1% from 6/14
4579 6/15 100.35% 100% decreased by 1% from earlier in the day
4584 6/17 100.46% 100%
4662 6/19 102.17% 102% increased by 2% from 6/17
4651 6/20 101.93% 102%
4456 6/20 97.66% 98% decreased by 4% from earlier in the day
4444 6/21 97.39% 97% decreased by 1% from 6/20
Your own screenshot from Coconut Battery shows the FCC fluctuations I mentioned (see chart I recreated above with added notes). In my own personal experience closely examining the battery FCC values, more than likely those changes are related to times when the laptop was under heavier load (battery draining more quickly due to high CPU load, or battery charging quickly), or the laptop may have been at 0% charge for a bit of time. Even the difference between the highest & lowest FCC values is only 218mAh (4662 - 4444) which is completely within normal behavior for an Apple Lithium Battery. That 218mAh difference is about 5% which is how macOS shows this information to users. I only become concerned when those FCC fluctuations start to go over 400mAh and then it depends on FCC behavior over time.
You posted here to get some insight and I have given you my insight & an explanation from years of personal experience where I have taken the time to observe lots of Apple Lithium batteries. Not many people have done this. If you search this forum, you will find a couple of other high level forum contributors who have posted something similar although in much less detail.
If you don't believe Coconut Battery (then why use it) or my own independent insight from personal experience supporting thousands of Apple laptops for years, then you should contact Apple directly for support. I doubt Apple will provide you the same level of details & explanations. Apple will just say everything is Ok & send you on your way after perhaps running their MRI service "diagnostic" which will report everything is good. FYI, Apple won't both with any information reported by third party apps and will just refer you to the information provided by the macOS GUI. Maybe this is not what you wanted to hear, but it is how these Apple Lithium Batteries behave.
Like I said before......unless the laptop's battery is not performing to your expectations, then just ignore any battery health information macOS provides to you including the "Service Recommended" battery condition. This battery information is only relevant when the battery is not meeting your expectations. Of course if you want to learn more about how your laptop's battery behaves, then please use Coconut Battery and monitor the information it & macOS shows you since that is how a person learns. That is what I had to do, although I used the built-in macOS command line utilities to get & monitor these details.
