Simply embed the 'update' feed on a page in the existing website and have some kind of admin panel where employees can easily CRUD some updates.
I guess because even this would not be 'free', twitter ends up winning.
In my experience this is usually the crux. That software always rots, and needs whatever (minimal) on-ramping for employees, as well as access management.
If I could wave a wand at those solutions I'd stop fighting the user and let them post to Twitter or wherever, and just have a public facing page pull those posts as updates for consumers outside of whatever walled garden they originate from.
Won't happen in the US/UK because the governments are in Elon's pockets. Won't happen in the EU because they are incapable of getting anything done.
So unless you're in a jurisdiction other than the above three I wouldn't hold your breath about any laws being passed about this.
A lot of private companies do the same thing - no way to effectively contact them privately, but as soon as you whinge publicly on X they're "on it". Octopus Energy is one of the worst for that.
That said, RSS seems way simpler.
RSS aggregation seems like the solution to me but I think we've got to admit defeat on that one because it's been around forever and people don't use it.