There's a lot of risk to striking for a federal worker. First of all, it's against the law for any employee of the US Federal Government to do so according to 5 USC §7311
An individual may not accept or hold a position in the Government of the United States or the government of the District of Columbia if he-
...
(3) participates in a strike, or asserts the right to strike, against the Government of the United States or the government of the District of Columbia; or
(4) is a member of an organization of employees of the Government of the United States or of individuals employed by the government of the District of Columbia that he knows asserts the right to strike against the Government of the United States or the government of the District of Columbia.
There exists federal employee unions, but they don't have as much power because they can't strike. Additionally, there's another US code (18 U.S.C. §1918) that reinforces this idea, also noting that it's a felony that can carry the charge of a fine or jail time up to 1 year and prevents you from being employed by the Federal Government (using the exact same language).
Additionally, the Office of Management & Budget can name you "unsuitable" for Federal employment if you participate in a strike even without the felony conviction.
This happened in the 80s when a bunch of Air Traffic Controllers went on strike for higher wages and the President at the time (Ronald Reagan) just fired them all and hired new controllers at lower wages who wouldn't strike. There was no recourse for those fired workers.
Given all of this, I wouldn't even risk it with DOGE to strike right now. Under a more labor friendly administration, you might be able to get away with it. But with Musk running the country, the most likely outcome would be that they'd fire them all for striking, the courts wouldn't restore them like they have with others because they did actually violate the law, and Musk would spin it as locating and eliminating the "corruption"
P.S. - For those keeping score at home, both of the aforementioned US codes are the same codes that bar someone for working for the Federal Government for advocating for the overthrow of the government (that's what subsections (1) and (2) state). Yes that means the Federal Government, at least as far as its own employees are concerned, equate striking with revolution
Unfortunately for Americans too, solidarity striking (the main premise behind being able to perform a General Strike), is also illegal (most citations I could find cite 29 U.S.C. § 158(b)(4) though I couldn't work out specifically what verbage outlawed it). Keep in mind to that this specific labor law only applies to private labor unions that are administered by the NLRB, federal unions have a different agency.
I know a few people, including a family member, that work for the federal government, and I think they want to try to weather the storm, but it's hard. Trump wasn't a fluke in 2016 and he certainly isn't one now. Just because he and his party might be out of power in 4 years doesn't mean much. Half the country still thinks their jobs and livelihood are superfluous at best and harmful at worst. And with four more years of the hack and slash mentality going, it may take a while to rebuild all of this. To get from the precursors to the New Deal through to the EPA was almost 50 years of slow progress.
One thing that I think doesn't get pointed out enough is that for the United States, the number of federal employees (pre-Musk) is basically the same as it was in the early 60s. The actual size of the federal government hasn't changed in 60 years by any appreciable amount. All that extra revenue and debt in the budget has gone to federal contractors.