So our concerns are that water is a part of our processing and we need to verify and show adequate cleaning methods affecting equipment that the water comes in contact with as well as when it hits our packaging product internally. - It is fine to test the city water coming into the plant; - we have that covered. But from point of facility entry by the city to coming in contact with product is the concerns.
In some respects, the answer is identical whether yr interest is internal or external.
The answer to "red" part is IMEX easy. Implement sampling/analysis of yr water at point of internal usage. This is a routine requirement in BRC Standard but SQF I'm unsure, i anticipate the same. Typical SOPs for sampling step are available and may also be detailed within the framework of the legal requirements discussed below.
The answer as to analysis for what depends on whether you are considering safety only or including non-safety factors (ie the current SQF Lvls 2/3)
I assume yr objective is safety only.
Then, afaik, the Global HACCP requirement is basically simple - process ingredients must be "Food-Grade".
For water, the legal interpretation of "food-grade" is typically that it must comply with the relevant Drinking Water Standard. (Legality is always the No.1 prioritised FS Standard criterion).
So you presumably require a Consultant who is aware of the relevant Local/Destination (assumed USA) US legal analytical requirements for classification as Drinking Water (I'm not aware if State requirements legally over-ride Federal for this case).(IIRC the published US Federal Requirement involves measurement of something like 10-15 items [as compared to the EC food import requirements of around 50!])
Hopefully all reputable US Consultants will be familiar/knowledgeable with the above.