First, I am an accountant. Well, that’s my job title at least. And I passed the CPA exam.
Assets are current possessions (possibly intangible) which can bring future positive financial outcomes. Liabilities are current obligations that can bring future negative outcomes. An obligation can never be an asset, and a possession can never be a liability, except if by law there is some obligation in how one disposes of that asset, which can definitely be the case for things like underground storage tanks. In that case, one accounts for an asset retirement obligation - see that article for the accounting of such an obligation. I greatly detest articles that say things like “Inventory is a liability”, because if it was, you would just get rid of it and would be better off. Inventory is simply an asset that is not as liquid as cash. Some possessions, like a contract right, might be tied to an obligation as well, but that contract right is the asset, and the obligation of performance under the contract is a liability if you gain access to that contract right before your own performance.
The use of "current’ in both definitions is meant to avoid issues of contingent liabilities and assets. The right to a possession later can be an asset if you have that right currently. If you contingently gain that right upon some contractual performance, it’s not an asset (and you don’t have revenue) until your performance under the contract. Likewise, entering into a noncancelable lease agreement (ignoring capital leases) gives you the obligation to make future payments, but they are not liabilities because the lessor has not performed their part of the contract yet - they haven’t let you had beneficial use for the prescribed time period until that time period actually elapses. Since leases are generally paid up front and not in arrears, you may actually even have a prepaid expense asset for a short amount of time, though not long enough to generally matter much; if there’s a refundable security deposit though, that’s an asset even if you can’t get access to it until the lease is up, because it’s a current right to receive money at a future time.
And so your work history on file with the Social Security administration along with your pulse are an asset to you, because together they will bring you a positive financial outcome: you’ll simply be given money for no consideration. Not a very liquid asset, but an asset. As mentioned, there are calculators that will tell you what it would cost you to replace that income stream if for some reason the government stops all SS payments immediately, and that is a reasonable guess as to the current net worth. I’d shade it down slightly, because whoever is offering the annuity also has to make a profit, but at the same time one can argue that you should shade it up slightly because the credit risk is much lower with the US government than with someone selling annuities, so you wouldn’t pay as much for a private annuity as you would for a government-backed annuity. So it’s a pretty good number to use.
Should you include it in your net worth? Well, that depends on why you want to know your net worth. If it’s simply to compare to other people, you need to know if the statistics that you’ve found elsewhere were compiled under the assumption that the future SS benefits were treated as a present-day lump sum. That’s on you to find out from your sources.
In terms of accounting for payments from the annuity, I would suggest that you simple credit it as revenue and then make an adjustment to the value of the remaining payments based on current annuity prices, as opposed to thinking about the money received as a draw against the asset. In terms of net worth, I wouldn’t count the annuity at the cash forfeiture value but at the replacement value just like SS, though you would include such an immediately payable amount as a current asset, as opposed to the excess value which you would classify as non-current, if you were doing a personal balance sheet.
In general, if you want to calculate the present value of an income stream with characteristics that are not currently defined completely, you need to develop a probability model for each of the possible outcomes, and discount future cash flows based on their likelihood of occurring. That’s what actuaries do, and they’re paid a lot of money to do it. That’s where the prices of the replacement annuities come from. It’s very complex financial mathematics.