I set the Web Audio script processor buffer size 1024 samples (23.2 ms), but this is too large for real-time performance. 512 samples buffer causes occasional noise, and 256 samples causes complete noise on my PC Chrome.

If you want to create a "playable" instrument, you should choose an appropriate native platform and programming language. For example, iOS Core Audio and Objective-C/C++ can achieve stable 128 samples (3 ms). That is the reason iPhone has many musical instrument apps.

ref. Android’s 10 Millisecond Problem explained | Hacker News

Due to the restriction from Chrome 71, we need to create AudioContext when a key is first pressed.

I've shared the showcase page with a friend and he couldn't play any sounds, and it turned out to be that the audio context was created before any user gesture, and it would be created suspended and it wouldn't play any sound.

You can add a function getAudioContext() and that function can create the context only when it is first needed (i.e. when a user presses a button or a key), and then store it in a global variable and just return it next time. The other thing you can do is capture all user gestures and do a context.resume() on at least the first time that event fires.