I started thinking about this after noticing something that does not get discussed much when people talk about money. Sometimes having little money can actually make certain things more expensive. For example someone with enough funds can buy something in bulk when the price is better and someone who is low in funds may have to keep buying smaller quantities at a higher cost.
Having available funds makes it possible to secure more favorable deal terms. That is true.
Someone with savings can take there time looking for a better job while someone who needs money immediately may have to accept the first opportunity available even if the pay is poor or the conditions are bad.
A person who lacks financial freedom becomes a "slave" to current circumstances and is forced to "pay" more (by foregoing potential profits, wages, or better terms).
Even with emergency having some money available can allow you to fix a small problem before it becomes a bigger and expensive one.
That is why you should always have some money set aside for a "rainy days".
So maybe money does not only buy things, maybe money only buys flexibility and that flexibility can sometimes allow someone to make easier decisions.
Of course, it is not merely a means of purchasing goods (or services), but an instrument of "freedom". Not just financial freedom, but freedom in the broadest sense - for with sufficient funds, you are not constrained in your actions as you would be by a lack of money. You can go wherever and whenever you please and do whatever you wish or implement the projects you wish - that is precisely what freedom is.
This is where I find the idea interesting. We often tell people to make better financial decisions but how much of that decision making actually depends on having financial freedom in the first place?
The more money one has, the greater the freedom of action. A person with no money to spare and someone with a financial reserve possess vastly different levels of freedom.
Does having money give people an advantage beyond the money itself because they have more options available for them?
Of course, they provide an advantage, for money is also a tool of "opportunity". (New) opportunities - for instance, to carry out projects (creative, charitable, business, etc.), that would have been impossible without money. In other words, money can provide, for instance, creative freedom in realizing one's abilities and ambitions.
And if that is true, could one of the hidden cost of being poor be that you have fewer opportunities to choose the easier option?
In a sense, yes. You could consider it an additional negative effect that compounds the poverty.
The miser pays twice, the fool three times, and the poor - always (to paraphrase folk wisdom

).
I’m curious how other see this. Is financial flexibility itself a form of wealth?
You certainly can, and I agree with you, for this financial flexibility allows you to preserve your wealth (by spending less than you otherwise would have). The essence of wealth lies not only in acquiring it but also in not losing it - in preserving it.