How are they gonna trace that to you?

The modern Internet is essentially about spying on you as much as possible and then selling the data to whoever wants to buy it. Linking identities with devices/browsers is worth a lot of money and so most every website/app has a way of linking you to the devices and software that you use.

Unless the user took some pretty extreme measures to create the account, they've likely logged in from a phone/ip/browser that has been linked to their real identity at some point in its lifetime. That link will be sold to data brokers and used to tie the random handle to you, the person. Then the State Department just buys that information.

Alternatively, you should be assuming that sovereign entities with the means are reading all public network data. There's a lot of information that you can learn from that as well. Like, over time, the posts from the 'random' account could be strongly correlated to the times that you were accessing the site even if all of the data was encrypted with HTTPS.

Alternatively, alternatively. There is a threat known as Store Now Decrypt Later (SNDL). The idea is basically: Quantum Computers are coming and they can break some cryptographic primitives. If someone saves all of the encrypted traffic that they would want to read, in a few years they will have the means to read that data. We won't know when this moment occurs, because it'll likely be a secret, but we do know that it will happen and so you should additionally assume that anything that isn't using post-quantum encryption, which transited a public network, will be read and used to link you to your identities.

This is, essentially, the core thing that the Privacy community is attempting to mitigate.