To the extend that it does have real word impact, is that because positive different from negative or just the absolute value equal to zero is different from nonzero?
A big surprise of the aftermath of 2008 is that investors will, in fact, tolerate a slightly negative interest rate. Big investors with tens of billions of dollars cannot simply take the money as cash, they need to put it in a bank, so if a bank imposes negative 0.1% then some investors simply consider that a fee for storing the money, so it was, in fact, possible to go slightly below zero. But the problem was, there was no way to go deeply below zero. In the USA in 2009 it was estimated that we would need an interest rate of negative 6% to get back to full employment. And of course, no investor will voluntarily take such a loss on their money. That's why monetary policy has limits. That why financial policy has to be used. However, a coalition of Republicans, along with a handful of key Democrats, such as Larry Summers, moved to block all financial policy, so we suffered several years of high unemployment.
Japan, of course, had it worse than the USA, as they are also facing demographic contraction. In their case, they used monetary policy and some financial policy, but all of it together barely offset the demographic contraction of working age adults that they have faced.
Its meaningfulness scales with the prevalence of physical cash.
If a society is cash heavy, negative rates incentivise taking out physical cash (which yields a nominal zero and thus positive-real rate.) If you can dissuade people from doing so, by law or inconvenience or the non-existence of cash, then the zero bound is mostly symbolic.
When the discount rate is negative, the value of an asset is infinite.