Johan

If I were putting odds on this, I'd put 85% on the solenoid, and 15%
on the wiring (usually connections at solenoid or starter), returning
ground to the battery connections, and starter (when the bearing
finally lets the largest diameter part touch the stationary field
plates the friction is high but the noise is low, but that's not
likely since it came on so fast).

The solenoid is a little heavy duty electrically powered plunger with
a larger electric switch capable of handling a lot more current than
would be elegant for car designers to mount on you dashboard or
steering column.  The heavy duty contacts are your PRIME suspect.  The
take a hell of a beating from all that making and breaking of high
current demands that occur at the beginning and release of your
starter switch which calls to the solenoid to 1st make and 2nd break
contact.  Both events cause sparking and microscopic metal removal of
the contact on each side.  I hope you have the picture.

Ok, while I haven't been into a VW solenoid, the principals are almost
universal.  On many old General Motors solenoids, they had a
stationary contact for one connector, and a rotating disk on the
other.  This disk would eventually get looking like the surface of the
moon and some junk would form on there so it had non-conductive
spots.  Successive attempts engaged different points along the disk,
so you had lots of warning that it was time for corrective action.  We
used to take it apart and flip the disk because the other side was
brand new.  Then we'd "dress down" the other contact with a file
anything other than sandpaper.

DON'T USE SANDPAPER TO DRESS HIGH CURRENT ELECTRICAL POINTS.  We can't
see the particulates sandpaper leaves behind, but these contaminants
severely shorten the service life of high current contact sets.  While
the studies that covered this topic haven't been popular since 40 to
60 years ago, their validity is unaltered.  Us a file or "burnishing
tool" which do not leave these contact life shortening contaminants.

All the best to you,
John