My battery health went down to 97% in 1 month

After 7 months the average iPhone Maximum Capacity will be 93%, so yours is ahead of the curve.

A battery is a chemical device, and chemistry is generally pretty variable and uncertain, as well as being analog, not digital. Apple specs the battery capacity to remain above 80% for 500 full charge cycles, but that is a minimum requirement; there is no published maximum expected capacity. So sometimes batteries will perform much better than that minimum specification, and sometimes the change in maximum capacity won't be linear. There is no way to predict in advance what the real-life performance of any specific battery will be.

All iPhones have a specification for the battery. As an example, for the iPhone 14 Pro that is 3200 milliampere-hours (MaH). So the battery monitor is calibrated for 100% at that value. But there are variations in manufacturing, so some batteries will have less capacity, and some will have more. Suppose your battery had, say, 3520 MaH capacity (10% over standard). That would still show as 100% (even though it was actually 110%), but as it aged the health would stay at 100% until it fell below 3200 MaH. This would appear to you as if the battery had fabulous life, until suddenly it didn’t.

Nothing wrong. You can expect a drop of about 1% per month on average. That does not mean every month will see a 1% drop and sometimes there will be none and other times there will be more. Since you are 6 months in with only a 3% drop, you are far ahead of the average. Just enjoy your iPhone and when the health drops below 80%, then it will be time to have it replaced. No need to micromanage the Battery Health, just use the Optimized Charging option and charge on a regular schedule so the phone can learn your charging habits. Usually this is best to be done every night.