Both `OutputSweeperSync` and `LiquidityManagerSync` added `Arc`s to
their internal state to allow returning a reference to that
internal state in testing. While this is required to get a
forever-lifetime reference to that state, we don't actually need
that in testing.

Instead, we turn off the borrow checker in the
`lightning-background-processor` async tests where required,
avoiding the extra heap indirection.

There's no need for these given `DefaultTimeProvider` is a unit
struct.

`OutputSweeper::new_with_kv_store_sync` is a pretty strange API -
it allows building an async `OutputSweeper` where the only `await`s
are on a sync `KVStore`, ie will immediately block until the IO
operation completes.

While this isn't broken (futures are allowed to take their time,
and async runtimes have to handle this, though they often don't
handle it particularly well), its pretty weird. It seems to exist
largely for `process_events_async_with_kv_store_sync`, which does
async `Event` handling but sync `KVStore` operations (like the
existing pre-0.2 "async" background processor).

Instead, we allow passing an `OutputSweeperSync` to
`process_events_async_with_kv_store_sync`, keeping the API
consistent such that a user would use the appropriate
`OutputSweeper` variant, but fetching the inner async
`OutputSweeper` inside the BP.