Not familiar with the term "vendor onboarding". i assume you mean the ultimate supplier.
Yr query is rather "open-ended" I deduce you are effectively acting as a QA Manager for Purchased food raw materials.
I'm not in USA/restaurant business but i suppose the documentation which might be involved is -
(a) that which may be Local Regulatory required, if any. No idea on that one.
(b) that which may be required for any private FS Standard which you wish to be audited/certified to. I deduce this is currently zero.
(c) that which you personally consider apprpriate to a/your "QA function". Below mainly addresses this.
A generic answer to yr general query is that specific requirements may be risk related, ie it depends on the product's individual risk assessment.
A processor certified to a GFSI-recognised standard should have been "satisfactorily" audited to most of yr list with exception of first one which I understand is a (semi-meaningless) US tradition.
Some buyers use Questionnaires similar to yr list (typical HACCP System components) in lieu of doing a direct audit. Typically for (considered) "Low Risk" items. However some Manufacturing facilities restirct such items to on-site customer viewing only.
IM(processor)EX (non-salmon) some buyers automatically require detailed internal COAs/agreed procedures for every lot supplied and some do not. It often depends on Company "Policy". And perhaps risk status as noted above.