Regarding battery health?

Batteries are consumables; they lose a little capacity every time they are discharged, then recharged. On average this works out to about a 1% loss for every 25 “full charge cycles”. As one example, if you charge the phone overnight, every night (and that is what you should do; it is a best practice), it starts the day at 100%. If it drops to 20% by the end of the day before you charge it again overnight that counts as 0.8 full charge cycles (20% to 100%), or about 24 full charge cycles per month of use. For this example your battery capacity will lose about 1% per month. Of course, if the end-of-day level is higher than 20% the capacity loss will be a little less, and if it is lower than 20%, or you charge it during the day, the capacity loss will be higher.

Once the capacity drops below 80%, or if there is a message in Battery Health that the battery is not meeting peak performance expectations, it’s time to change the battery→iPhone Battery Replacement - Official Apple Support

The absolute best way to get maximum use on a charge, as well as slow the decline of battery capacity long term is to enable Optimized Battery Charging (Settings/Battery/Battery Health) and charge the device overnight, every night. The battery will fast charge to 80%, then pause. During the nighttime pause the phone will use mains power instead of battery power, allowing the battery to “rest”, and thus reducing the need to charge the battery quite as often. The phone will resume charging to reach 100% when you are ready to use your phone; it will “learn” your usage pattern. If you enable iCloud Backup (Settings/[your name]/iCloud - iCloud Backup) the phone will back up overnight also, assuring that you can never lose more than the current day’s updates. Here's more information→About Optimized Battery Charging on your iPhone - Apple Support

Hello,

I don't think a 3% drop in a month is very uncommon or concerning. Below I have included a few links and quotes for you to get more information if you desire.

iPhone Battery and Performance - Apple Support

"Maximum battery capacity measures the device battery capacity relative to when it was new. A battery will have lower capacity as the battery chemically ages which may result in fewer hours of usage between charges. Depending upon the length of time between when the iPhone was made and when it is activated, your battery capacity may show as slightly less than 100%.

A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge. Learn more about charge cycles."

If the games you are playing have very detailed and high intensity graphics they could be the main culprit for the reduction of your battery capacity. You could adjust some settings or use Low Power Mode to reduce the battery stress but it would likely have an effect on the game graphics.

Batteries - Maximizing Performance - Apple

"Optimize your settings.

There are two simple ways you can preserve battery life — no matter how you use your device: adjust your screen brightness and use Wi‑Fi.

Dim the screen or turn on Auto-Brightness to extend battery life.

• To dim, open Control Center and drag the Brightness slider to the bottom.
• Auto-Brightness adjusts your screen to lighting conditions automatically. To activate it, go to Settings > Accessibility. Tap Display & Text Size, then turn on Auto-Brightness.

When you use your device to access data, a Wi‑Fi connection uses less power than a cellular network — so keep Wi‑Fi on at all times. To turn on Wi‑Fi, go to Settings > Wi‑Fi to access a Wi‑Fi network.

Enable Low Power Mode.

Introduced with iOS 9, Low Power Mode is an easy way to extend the battery life of your iPhone when it starts to get low. Your iPhone lets you know when your battery level goes down to 20%, and again at 10%, and lets you turn on Low Power Mode with one tap. Or you can enable it by going to Settings > Battery. Low Power Mode reduces display brightness, optimizes device performance, and minimizes system animations. Apps including Mail will not download content in the background, and features like AirDrop, iCloud sync, and Continuity will be disabled. You can still use key functions like making and receiving phone calls, email, and messages, accessing the Internet, and more. And when your phone charges up again, Low Power Mode automatically switches off."

I hope this helps.