There seems to be a number of vacuum related parts in the middle of the plastic intake manifold on the 1.6L engine; you might wiggle different parts, trace the vacuum lines, check parts # (8, 9, 4, 3) and put a rag on things, see if the sound changes? This might help narrow down; where the sound is coming from and possible vacuum leaks?
If you don't have a service manual; you should consider getting, the UK version of the Haynes manual, not as good as eRWin factory VW manuals but it does cover the 1.6L engine:
Volkswagen New Beetle (1999 - 2007)
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