Drop the `no-std` feature from BP and drop feature implications

Drop the `no-std` feature from BP and drop feature implications

Now that we don't have to have everything in our entire ecosystem
use the same `std`/`no-std` feature combinations we should start by
untangling our own features a bit.

This takes the first step by removing the `no-std` feature entirely
from the `lightning-background-processor` crate and removing most
feature implications on dependencies from the remaining `std`
feature.

It also addresses a CI oversight where we were not testing
`lightning-background-processor` without the `std` feature in CI at
all.