Startng with the iPhone XR, Apple started pairing the battery to the logic board. No, there isn't any reason to do that other than to discourage self- and third party repairs.
Since Apple is the only one who can do that parts pairing, any replacement, even when done with a genuine Apple battery, is going to result in the messages you're seeing. It's my understanding the pop-up messages will stop in about a week, but the badge on your Settings icon will be permanent.
In addition to the genuine parts message, the ability to view your battery health information is disabled, making it difficult to know when the next time you need to replace the battery is.
There are, however, ways around the issue. One is to transfer the BMS, or Battery Management System, from the old battery to a new cell. This will keep the warning message from coming up, and allow you to keep viewing the health info, but unfortunately it will carry forward the old battery's health information, which will now be wrong.
In the case of a genuine Apple battery, Apple has relented somewhat with the release of iOS 18 and included the Repair Assistant that will let you pair your new battery to your phone, fixing the issues. Sorry to say this won't help you with your aftermarket iFixit battery; to the best of my knowledge I am fairly sure iFixit does not sell genuine Apple parts.
You could also make use of the Apple self repair program, but my understanding is it's not that much cheaper than just going to the Apple store and having them replace it.
The upshot is that you didn't do anything wrong; Apple is deliberately putting obstacles in the way of you being able to fix your own phone.
Now, on your other issue, that of the short battery life, that sounds like an issue with the new battery. The good news here is that iFixit has an outstanding 1 year warranty on batteries and you shouldn't have any issue getting a replacement under warranty. Best way I know of to contact them regarding the problem you're having (the life of the battery, not the health/warning issue) is to email them at support@ifixit.com. I've found them to be responsive and helpful when I had a battery issue with one I bought from them.
I should add that other than the warning message and the health information, any replacement battery, whether genuine Apple or not, will charge and power your phone without any other problems.
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