Battery and Display both "Not Recognized"

From the inception of Touch ID on the iPhone 5S and Face ID on the iPhone X, Apple has paired the parts associated with that functionality to the motherboard such that only Apple can replace those parts and have them continue to function. For Touch ID, that consists of the home button, while Face ID is much more complicated, including the front camera assembly and the earpiece speaker assembly.

Apple gave the excuse that the pairing was necessary for security to ensure no one could hack the hardware and defeat the ID system. We tended to accept that grudgingly, although with some suspicion due to the fact that other manufacturers do allow you to replace things like the fingerprint sensor on a Google Pixel phone, for example.

However, beginning with the iPhone XS, Apple began to get more aggressive with their parts pairing policies. On that phone they began pairing the battery to the motherboard, with the result that replacement of the battery, whether done with genuine Apple parts or not, results in a couple of issues. First, as you've already found, you'll get the pop-up warning when you power up the phone for about a week or so, which will eventually go away. However, the badge that appears on the Settings icon and the associated warning under the Battery section will be permanent. Most people can live with that, but Apple has chosen to disable the battery health information when the battery isn't paired with the motherboard, so you no longer have access to important diagnostic info that can tell you when you need to replace the battery.

The aftermarket industry found that you could disassemble the BMS (Battery Management System) from the original battery and transplant it to a replacement battery cell and that would bypass the non-genuine parts warning and allow you to keep your battery health information. However, the issue here is that the battery health is kept on the BMS, so even though your battery cell is brand new, the health information will still reflect that of the original battery. There are device programmers on the market for as low as $35 or so that will allow you to reprogram the battery health to 100% and the cycle count back to zero.

So now all is well and good again, right up until they release the iPhone 11. You can still replace the battery cell giving you a brand new battery, but in the spirit of keeping people from being able to fix their own phones, Apple has now changed the way the battery health information is stored such that it can no longer be reset with a device programmer! Yes, a true dick move on their part. However, once again the aftermarket industry stepped up and invented something called a tag-on flex cable; it's a tiny circuit board similar to the BMS that plugs in between the battery and the motherboard. Once it's installed on the battery, you can now use the device programmer to reset the battery health; the catch is the tag-on flex has to be installed in the phone permanently in order to work. I don't know of any downside to doing that so it doesn't seem like a problem. Later models even come with the battery health information already reset so no device programmer is required to use them.

Of course, I glossed over the actual replacement of the BMS, a procedure that requires removing tape, carefully unfolding the battery packaging, then cutting the BMS off the cell. After that you have to either solder or spot weld the BMS onto the replacement cell and refold the packaging and reapply any adhesive tapes in use.

That covers Apple's anti-repair moves for the battery, but don't forget the next-most-often-replaced item on the phone, the screen. Yep, starting with the iPhone 11, they also started pairing the screen to the motherboard! This one is much more difficult to work around, as the pairing information is kept on the touch screen module, a BGA part that has to be carefully desoldered from the original screen and installed on the replacement. Unlike the battery workaround, this one can't really be done by us home DIY-ers, leaving us with the choice of either living with the warning or paying Apple to replace the screen. Unfortunately, you're just one generation too early to be able to use the self repair option, as that didn't start until the iPhone 12. Even then it's not that great of a deal, since you still have to pay full price for the genuine Apple screen, then you have to rent Apple's equipment so you get access to their "calibration tool" to do the parts pairing. So it's only marginally cheaper and you end up having to do all the work, plus picking up and returning their equipment.

There is one other issue with replacing a screen on an iPhone, and that's the True Tone function. Once you replace a screen you will lose the True Tone function that was introduced on the iPhone 8 and all later phones. Once again, it is possible to use a device programmer to read out a piece of data called the MtSN from either the phone itself or the original screen and reprogram it into the new screen, restoring True Tone. It's kind of a half-assed form of pairing where the function won't work unless the numbers match, but they didn't use a proprietary encryption algorithm so the number can actually be copied. Those programmers are more expensive than the battery programmer; as I recall I paid about $80 USD for mine, but it does have the advantage of programming both screens and batteries.

So there you have it, parts pairing being aggressively pursued by Apple for the sole purpose of keeping aftermarket parts and repair shops out of the business of repairing iPhones. The later the model phone, the worse the pairing gets; the iPhone 14 is an absolute disaster for repair shops and people who want to fix their own devices. On that one the following parts cannot be replaced without a parts warning and/or a loss of function: Face ID, Display (with True Tone), Battery, Rear Camera, Selfie Camera and the wireless charging assembly. If I'm not mistaken, the iPhone 15 is as bad or worse.

Sorry to tell you, but without the original battery the only way you're going to get your health information back and get rid of the warning is to pay Apple to replace the battery, and ditto for the screen. Apparently they are relenting on this approach somewhat due to right to repair laws that are trying to make it unlawful to use parts pairing to discourage aftermarket parts and repairs, but any changes they make won't help unless you have an iPhone 15 or later.

P.S., Nothing that was done would cause your memory to be reduced; you can check the IMEI number against your original purchase receipt to verify you got the same phone back, but I strongly suspect you've just misremembered the amount of memory on the phone.