Brooklyn voter here.
For what little it's worth, the instructions on the ballot said to use a black pen to mark the ballot. I noticed as I was walking by that some of the voting booths were missing pens, and some had blue pens, some had black pens, and some had multiple pens with different colors. I used a black pen.
Wish I asked about it and documented it at the time, but just mentioning it for others to see if anybody else has any thoughts. At the time I was focusing on filling out my ballot correctly and just trying to watch the flow of people and the voting workers to see if anything untoward was going on and I didn't think too much of it. But now that Arizona is mentioning the sharpie thing, that really activated some almonds.
Not that New York is likely to even come close to being in play, and I don't know what effect that would have on the vote being counted, but it seems odd that if the vote counting machines have writing black pen instructions that they'd have multiple color pens at the booths. I looked up some 3rd party voting FAQs and they say that that blue or black would be fine, but why did the ballot instructions specify black if any color would work? Just seems odd and mentioning it in the very unlikely case this is important.
TLDR: Blue ink probably ok as far as modern scanners go.
Modern OCR scanners read reflections. They can usually read almost any marks. They read from one side and can process both sides at once as well as forms printed on thicker paper.
Older scanners where you needed the proverbial #2 pencil, read through the paper. These were already going away in the 1980's. They needed the carbon content in the pencil in order to work and thin enough paper for the light to pass through it. They could do double sided, only if bubbles and marks didn't overlap and you ran both sides through separately.
If none of the voter marks on a ballot were readable, the machine probably would have kicked out the ballot as blank.
Blue ink was probably ok. Where it may have been not as good as black, is for marks that don't fill the entire bubble.
The ballots here said use a black pen too, but due to the wuflu, they passed out one-time-use golf pencils in the elections this year and we had extras. Worked fine.
You describe pens were at the booth where you fill the ballot. I suppose if everyone was handed a pen, they could hand blue ones to some people and black ones to others to be able to identify ballots later on for 'special processing' during a recount. In your case, the booth you voted in was chosen by the voter not assigned so different color ink would be meaningless.