John 6 does not say that faith is "a work", and with respect to you and everyone else who has misread it, it's not primarily about the nature of faith at all. Let's look at it closely:
(After the feeding of the 5,000)
28 Then said they [the people] unto him, What shall we do, that we might work the works of God?
29 Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.
The people asked how they too could do the works of God (in context, getting food miraculously).
Jesus' answer was not "how they too could do the works of God", but what the work of God was.
In other words, Jesus was making clear that feeding people miraculously was not His primary intention. Rather, having people come to believe on Him was the "miracle" He desired.
This passage is NOT about faith being a work (or not a work); it is about the goal of Jesus' ministry.
I appreciate your perspective, but I see it differently.
In John 6 Jesus said that He is the bread from Heaven, comparing Himself to the manna given to Israel while they were in the desert. Israel had to gather the manna, refine it, cook it, then eat it or they would have starved. So while the manna was given to them freely, but they had to work.
I agree with you on the point that they were wanting more food from Jesus and they were working to get it, but Jesus told them not to work for food that perishes but rather work to believe in Him. Jesus told them,
John 6:27 Do not work for the food that perishes, but the food that remains to eternal life, which the Son of Man will give to you. For God the Father has set his seal on this one."
The reason Jesus was telling them to believe in Him was because they weren’t believing in Him. They needed to believe in Him to access the “bread from heaven” and work for it just like Israel worked for their bread.
John 6:36 But I said to you that you have seen me and do not believe.
So what I believe Jesus meant was that if they wanted to work the works of God, like how Israel worked for their bread, they, too, needed to consume the bread from heaven by working to believe in Jesus.
For the comparison Jesus made between Israel working for their bread and Himself to be accurate, then work is also required to believe in Jesus. That’s why I take John 6:28,29 literally at face value.