Your management has handed down an unreasonable requirement.
There are two reasons this happens:
Someone in charge is so profoundly disconnected from reality that they simply cannot comprehend that things do not work the way that they wish they did. This is actually pretty rare.
That person does understand that nobody will actually meet those expectations, but believes that dangling the unachievable goal out in front of people will encourage them to work harder to meet it. This is far more likely.
If nobody can meet the requirement, chances are somewhat high that the requirement will shift - because this is in it's early stages, what you're currently experiencing is a likely calibration process for acquiring reasonable expectations.
Do your best to track your time honestly, try your best to make sure your colleagues are on the same page about how to address common 'oddities' with tracking time, and keep an open dialogue with your immediate supervisor and stay transparent about your difficulties with the software.
It is paramount to keep solidarity on your team so that your individual data stays consistent with regards to each other. If people start trying to game the system, you'll undermine management's ability to form realistic expectations based off the reality in front of them.
A few months in a large organization is a relatively short time. It is somewhat unsurprising that their expectations have not yet shifted - this is likely someone's pet project, and they are likely several degrees removed from anyone who is actually working, and have several layers of people in between who are afraid of communicating undesirable information to them.
Your antidote here is to make sure that ALL information that gets back up to that person is undesirable, as your only chance to change this is to make it overwhelmingly clear that their expectations cannot match reality.
Once this battle has finally been fought on fair and even footing above your head with real data, your org can start having reasonable conversations about whether or not this is even worth the effort, and what a reasonable bar to measure employee productivity might actually look like.
It is likely that process will take several more months to achieve any progress. Those months will be painful, and frankly if your management is incompetent enough to believe in this kind of time tracking, it likely is not worth the effort to try to salvage your position.
However, if you are invested in this specific position due to a lack of opportunity elsewhere or some other reason, and you've given this situation a few more months to settle into something more reasonable and it hasn't, your only remaining option is going to be to try to organize some kind of collective counter-action.
If your org has attempted to play ball, proven empirically that playing ball is not possible, and management still hasn't changed their position, the only way to shift the needle is via collective bargaining.