Judge says Education Dept partisan out-of-office emails violated First Amendment

I fundamentally don't understand the rights of government employees. They are supposedly there to execute the will of the political branch that controls them whether or not they agree with it, which is why they are given immunity from firing by each incoming administration. So how do they also have the right to personalized communication from their work email addresses (a right that no private sector employee has)? How can they have the right to exercise government authority without being democratically elected, or at least accountable for their actions to someone who is?

You're correct that you don't understand how those rights work.

I think you're actually struggling more with the idea that the First Amendment is a restriction on government, not on employers generally.

But the most relevant thing that you don't understand is that government employees are NOT supposed or allowed to act in partisan ways. Your suggestion seems to be that's the point of the job. In fact, that type of activity is prohibited in their official functions and can even be illegal.

But government employees obviously do not have 1A rights in their role as employees. e.g. if a government employee feels like wearing a nazi uniform to the office every day, they will be fired, even though 1A prevents the government from punishing private citizens for doing the very same. Firing the employee is not violating 1A but charging them with a crime would be.

And how do you define "partisan" here? How can your job be to implement the policies set by politicians, but not be "partisan."