Striesand Effect is about censorship/exposure and is not relevant to this case which is about seeking the identity of the poster presumably because they are a federal employee. It doesn't seem like they're trying to do anything quietly, just get information for now.
Trump has countless vocal detractors. Trying to silence a solitary one seems pointless, though I wouldn't entirely put that past this administration.
Am I misreading Streisand effect? Trying to prevent a fact from becoming well known causes it to become well known. The general message "Trump does bad things" is not a secret.
Suppose that were true. Then they would want to conduct this as publicly and noisily as possible in order to propagate that fear. Which would be counter to what Streisand Effect suggests.
You'd want to do this loudly enough that other dissidents hear and are afraid but not so loudly that other citizens get word and potentially join the dissidents' side. You don't want a public lawsuit. You want Twitter to silently hand over the data and for the last tweet from the account to be "Got fired today :(".
The core idea of the Streisand effect is when someone's response to criticism backfires and brings much more publicity to the criticism.
I guess if you truly believe the government was "just asking questions" or honestly investigating a crime without the underlying motive of hushing a pesky critic, then it wouldn't be an example of the Streisand effect.
