Do you have a pull up on the DHT20? If not that could explain the reliability issues. 4.7k is needed according to the datasheet.
Not too familiar with the RPi Pico but you might need to disable the internal pull ups if you do that but they are likely too weak so I wouldn’t rely on them.
Yeah on that specific board it looks like it’s included . I was just going from experience. I just wired such a sensor to an Arduino the other day and I was having problems without the pull up. I was seeing garbled data packets on the data line.
edit: you can easily confirm this by measuring the resistance between VCC and Data on the sensor.