I’m pretty sure you can’t take a short position against the interests of your own company. That’s boilerplate language in the deals I’ve seen, for obvious reasons.
Carl Icahn may have found a way around this kind of restriction after the Lyft IPO by selling in a private transaction to someone who hedged in advance of the sale, although it's not at all clear what really happened.
Some companies will allow this, but only if it's a covered call or protected put on an investment that you own. The idea is that you're limiting your risk while also limiting the potential upside of the investment.