Only filter.nostr.wine, not the regular relay.
The filter is a public relay aggregator that also filters spam. You can see the list of relays that get aggregated here: https://nostr-wine.github.io/filter-relay/
It also can broadcast your notes to the same relays depending on the string you use to connect. This has a side benefit of reducing battery usage on mobile by reducing the number of connections you need to reach the same number of relays.
If I am remembering correctly, #[2] has said the recurring cost is because it costs a good bit more to run filter than the standard relay, which tracks with my understanding of how it works.
nostr.wine will continue to work even if you chose to not renew the filter part.