Hi Faldar,
Welcome to Apple Support Communities. So we can clarify, do you only charge the device wirelessly? If so, do you experience the same thing when charging directly with the cable? Also, you may want to check that Optimized Battery Charging is still enabled on the device. Go to Settings > Battery > Battery Health > Optimized Battery Charging, and confirm it is set to On. More info on that can be found here:
About Optimized Battery Charging on your iPhone - Apple Support
Also, are you getting any temperature warnings on your iPhone 13? If so, some insight into that can be found in this Apple Support article: If your iPhone, iPad, or iPod touch gets too hot or too cold - Apple Support
"If your device gets too warm
iOS and iPadOS devices have built-in protections to prevent overheating. If the interior temperature of your device exceeds the normal operating range, your device will protect its internal components by attempting to regulate its temperature. Here are some of the higher ambient-temperature conditions and activities to avoid, because they might cause your device to change performance and behavior:
- Avoid leaving your device in a car on a hot day.
- Avoid leaving your device in direct sunlight for an extended period of time.
- Avoid using certain features in hot conditions or direct sunlight for an extended period of time, such as GPS tracking or navigation in a car, playing a graphics-intensive game, or using augmented-reality apps.
If the interior temperature of your device exceeds the normal operating range, you might notice these changes:
- Charging, including wireless charging, slows or stops.
- The display dims or goes black.
- Cellular radios enter a low-power state. The signal might weaken during this time.
- The camera flash is temporarily disabled.
- Performance slows with graphics-intensive or augmented-reality apps or features.
Additionally, if you're navigating, your device might show this alert and turn off the display: "Temperature: iPhone needs to cool down." Navigation still provides audible turn-by-turn directions. When approaching a turn, the display will illuminate to guide you through the turn."
Let us know if this helps you.
Best regards!