Apologies if am misreading the last paragraph, assuming it meant that it's hard to find the Pico, that was the case for a while but the situation is now much better, e.g. Adafruit has 56 in stock: https://www.adafruit.com/product/4883

Admittedly, this is $1 more expensive than the $4 baseline board since it also comes with headers.

Just checked and DigiKey has about 17K in stock ($4 Raspberry Pi Pico): https://www.digikey.com/en/products/detail/raspberry-pi/SC09....

And that's leaving aside the slightly fancier boards that have the RP2040 and cost around $10, e.g. Adafruit Feather RP2040 etc.

The chip itself is not in any shortage, e.g. DigiKey and Mouser have tens of thousands/thousands in stock, etc.