Hi Jerry - Adafruit frequently runs out of stock of popular items but in many years of purchasing from them they always get them back in after a brief time. You can sign up to be notified when it's back in stock and most likely they will have more in a week or two. For sure it has not been discontinued.
You will save yourself a lot of time and trouble by using the Adafruit version, but yes you can use other brands of Bluetooth modules, do a search on eBay or AliExpress or Amazon for "Arduino Bluetooth module" and you can find some for cheap and most of them should theoretically work, with caveats. You can read/write settings with these other modules but you will not be able to flash firmware updates with them. You may find them finicky, they may not have good documentation, you will need to be sure you wire them correctly (the pins are printed on the bottom of the TCB), and you will probably have to fool with various configuration screens in Windows before they work. One of the Russian guys got a module working with his computer, you can
read about his experiments here (use Google translate in Chrome to read it, works quite well).
I personally have not messed around with the cheap Chinese modules so I can't offer much assistance, but yes you can get them to work if you have the time and energy.