Audio cracking on web depending on server?

I agree this does seem to be related to performance, and HTML5 is notorious for performance issues due to its lack of threading support. Increasing the DSP buffer size is a good start, you could also try changing the Loading Mode of any streaming assets to Compressed or Decompressed.
For best performance on HTML5 you can try enabling SharedArrayBuffer, which can be set from the server header with Cross-Origin-Opener-Policy: same-origin and Cross-Origin-Embedder-Policy: require-corp policies.