BLE development on Arduino IDE?

Hope this is the correct forum for my question.

Does anyone know of BLE module support for the Arduino IDE (similar to the ESP8266 support provided through the boards manager feature)?

My need is very basic... it's a battery operated servo controller, so I'm attempting to do everything on the BLE module (receive a command from a smartphone over BT, turn a servo with PWM, and return a status over BT to the phone). I don't have a preferred BLE module/chip yet, as it comes down to power consumption, PWM support and development tools.

I've been searching for a couple days, but have not seen anything for Arduino IDE yet.

If not available on Arduino IDE, what other development platforms can BLE modules be developed on?

Which BLE module are you talking about? Does it have programmable functionality like that? Many of the bluetooth modules aren't programmable like that (just like most wifi and ethernet adapters)

The ESP8266 has quite a capable microcontroller built-in, so there's something to program. The ESP8266 is better thought of as a microcontroller that has builtin wifi than as a wifi adapter. The fact that they can be used as a serial wifi adapter is just because that's the program loaded on them by default.