Puck.js v 2.1 a not turning on

and pressing the button while putting the baattery back in DID give me a flash of all the leds and then, only once, continued with a flaash of the green LED three times.

Ok - so the green LED flash 3 times means it's started up into Espruino and hasn't loaded any code.

If you let go of the button as soon as any lights light up, you'll enter bootloader mode (green LED on solid). Which I think is what you need to do to solve the other issue you posted: https://forum.espruino.com/conversations/382940/#comment16827704

I guess I missed or misunderstood the need to press the button AS the battery is being inserted.

You need to hold the button down, then insert the battery with the button still held...

But to just use the Puck normally, holding the button isn't needed. Once the red LED flashes you should be ok to connect.

The puck still isn't recognized by my chromebook's pairing

No, it won't be. You need to go to espruino.com/ide and then connect from there - do not pair it from the OS bluetooth menu - and if you have done, you need to unpair it.

There is a tutorial on getting started at https://www.espruino.com/Quick+Start+BLE#puckjs and I think it'd be worth going through that step by step

Do you know if there's an espruino version of the madgwick ahrs protocol?

For do you mean https://github.com/arduino-libraries/MadgwickAHRS/blob/master/src/MadgwickAHRS.cpp ?

I'm not aware of an implementation but the code there looks quite straightforward (just a bunch of maths) so it would be almost copy/paste to get it running in Espruino (change float to var and remove f from the end of the numbers).