Replacing an existing ground rod
Maybe the electrician wouldn't just pop a clamp on there because there is too much not seen to the eye, he was confused, and didn't want his license to be on the hook without opening a big can of worms. (Also it looks like you may have some solar equipment, and that may be over his head or license.)
I would expect to see the water pipe bonded and two ground rods connected with #6 bare copper wire for a 150A service. The wire to the water pipe needs to be connected within 5' of where it enters the building. I would call the local inspector and ask if local ordinances requires the ground rods be further separated than the 6' required by the (2017) NEC. One jurisdiction I have worked in required 16'. It is acceptable to run separate Grounding Electrode Conductor (GEC) to each electrode. Usually you loop the GEC through the connector at the first ground rod and extend to the second. Then a separate wire is run to the water pipe, but you could extend the wire from the rods to the water pipe or pipe to a rod. Generally the conductors need to be continuous or spliced with irreversible connection. I would only use ground rods with a (UL or other) Listing mark.
Now some explanation and disclaimers. An unaltered system is legal as long as it was legally installed when installed. The open question that is left to local interpretation is &quot;when does a repair or addition trigger the requirement to bring something up to current code?&quot; So any advice here may exceed the minimum work you might be able to get by with, but will reflect what most electricians would expect an Inspector would expect to see. A local jurisdiction would likely require updating with the addition of solar equipment.
The cold water pipe used to satisfy the Grounding Electrode requirement. Then the Code was revised and said a water pipe needs a supplemental grounding electrode, which for most purposes means a ground rod. This is likely what was required when your electrical panel was installed. Then the Code writers decided that ground rods had to test 25 ohms or less to ground or a second ground rod at least 6 feet away is required. Also Communication systems, lightening arrest, and other systems need to be connected to the Grounding Electrode System, the methods have evolved also, and the NEC hasn't always been adopted or enforced by local jurisdictions or even interpreted the same. Sometimes a 5 ft. ground rod has been driven to satisfy those systems, but they don't satisfy the requirements for your electric service. A fuller mostly accurate description of current requirements for ground rods can be found here. Currently most jurisdictions have adopted the requirement of a Intersystem Bonding Termination for new services, you likely do not need to worry about that.