Ownership of private property (abstract or concrete) is a
formal, legally-defined concept — and "do you have essentially sovereign authority over the disposition of the asset" is always at the core of it.
No, you don't own stock when you own stock options. A stock option is a right to purchase stock at a particular price, and you own that right. Just like owning, say, an easement on a piece of land, doesn't mean you own the land. (And both a stock option and an easement have a value, and you may be able to sell those things themselves — but the value they have, and their sale price, is often disconnected from that of the underlying asset the right exercises against.)
You know how you can very easily tell when you own something? Because governments almost always tax transfer of ownership of a thing. You don't pay taxes when you acquire options, because you haven't yet acquired ownership over anything. You do pay taxes when you exercise those options — exercise that right to acquire stock at that price — because now you do own something you didn't before.
Another way to tell that you own a thing, is that you have the ability to directly pledge that thing as collateral on a loan. You can pledge stock, but you can't pledge options[1]. This is because you can contractually grant the bank the ability to confiscate your stock in event of default on the loan, in a way that guarantees that they will succeed in this confiscation. But you can't contractually grant the bank the ability to confiscate your options, in a way that is guaranteed to succeed.
And that's for exactly the reasons you outline: there may be contractual stipulation on the exercise of the options, that mean that the bank can't immediately liquidate the options, and thereby can't balance the loss-of-lendable-assets coming from your default and/or might risk the company's share-price falling, or even the company going bankrupt, before the options may be exercised.
Also, sometimes the bank wouldn't want to exercise a contingent asset they've acquired, but just wants to sell that contingent asset on to someone else who wants to hold and exercise it at a future date. ESOPs in particular usually have voidability clauses that say that not only can't you transfer the option, you can't even build a financial instrument around the option that has the semantics of transferability. Banks very much do not appreciate restrictions like that.
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[1] Yes, you can show your holding of options as a demonstration of assets, to increase the amount a bank is willing to lend you. But this, like any other demonstration of assets — e.g. a demonstration of employment, or of ownership of revenue-generating assets — goes into a Net Present Value-adjusted future-cashflow projection calculation that the bank does, to determine how likely you will be to be able to make your regular loan payments when everything is going well for you. In the breach, they still need collateral to be pledged out of stuff you actually own — i.e. can guarantee them the right to as a creditor.