Interpreting pull-up values Rp and Rpu in AM3202 (DHT22) datasheet
The datasheet is as inaccurate as the sensor itself and it is even worse than you think!

In that datasheet is also written: "usually require an external about 5.1kΩ pull-up resistor".

In the datasheet is also mentioned that the output signal can go up to 8 mA for a high output and minimal 10 µA low output. The 10 µA means that the pullup resistor should be 500k or more. That is not correct.

In this datasheet is a picture with 1k.
In this Chinese datasheet is a picture with 5k.
I ran that Chinese datasheet through Google Translate, but that did not help.

Conclusion: The datasheet is not reliable.

You can do as everyone else: use a 10k resistor for short wires, and try 4k7 for longer wires.

That is not the only problem. Some DHT libraries create a shortcut on the data signal.

The AM3202 is not accurate for measuring the humidity. If you want to avoid trouble, then use a better sensor.
A sensor from Bosch is a good choice (for example the BME280 or BME680). Bosch makes datasheets that are reliable. Those sensors from Bosch operate at 3.3V, if you are going to connect that to a 5V Arduino board, then you need level shifters for the signals.