Where I live those trust accounts are interest-bearing, and the interest is swept into a state-run legal aid fund for the poor. So it would be a (very slight) added bonus that Google's payment mistake would have some societal benefit.
Anyway, Google's fiscal quarter ends in ~2 weeks. They'll probably notice it when they reconcile accounts for SEC reporting, starting Oct 1.
$250k is rounding error territory at such a large organization. Not only that but the person in question is registered to receive bug bounties worth... $250k.
So no, I don't think they'd think twice about it when it comes time to reconcile the books.
So I guess the question then is: "at what point can you keep it/spend it without any legal concern?"
I know several accountants who do not work for trillion dollar companies. Variances in the millions are a daily thing. The more money moving around, the more unqualified people categorizing it and the more likely there is mystery money that cannot be rectified.
Realistically speaking the interest would get soaked up by the banks providing that account, because they'll be paying a pitiful rate[1] of 0.01% or whatever, whereas the prevailing rate for short term deposits is around 2.5%[2].
[1] random result: https://www.chase.com/personal/savings/savings-account/inter...
[2] https://home.treasury.gov/resource-center/data-chart-center/...