4Chan doesn’t have their own personal payment processor that they’re responsible for. They’re tied into processors like stripe and accept all payments that make it to them on the US side. So long as it is legal, which is typically the only way that a payment actually goes through as processors refuse the obviously illegal cases like encompassing embargoes. If the UK doesn’t want payments going to 4chan through a processor that operates in their country, it’s on them to stop the payment processor on their end.
The UK knows this, the fines are just one step towards them petitioning processors.
Settlements can go undisclosed by agreement of the parties involved. Civil court is different from criminal; the former is for the benefit of interested parties, the latter is for the benefit of the public at large. Criminal courts can do some things behind closed doors as well but that usually requires a need of the state (such as protection of a judge, jury, state, etc.)
This is assuming a legal system similar to that in OPs post.