It's 2,000 shareholders, and you are allowed to go above the limit, it's just that if you do, then you have to make public financial statements and in general follow all the disclosure rules and reporting requirements of a public company. Since it can be expensive to follow these requirements, especially for a startup that's not setup to do those sort of disclosures, startups will carefully avoid going over the limit. But since Twitter has already been public up until now, all the processes and institutional know-how to comply with those requirements is already in place, so continuing to comply shouldn't be too hard.
It was also my impression that holders of employee stock are not counted in the same way as normal shareholders, hence the tendency to limit third-party transactions of RSU shares. But I might be mistaken.
No, I can say from personal experience receiving RSUs from private companies that there was no arbitrary limit on how many people could receive them. I don't fully understand why that is the case, my suspicion is that employees receive share units, i.e. are not "shareholders" technically. The share units can be converted to cash at liquidity events or will convert to actual shares at an IPO event.
Why would this be the case? There are tons of tech companies (possibly even most?) that have more than 1000 employees at the time of IPO. As far as I know there are no limits on the number of shareholders for C-corps, private or not.