As mentioned, there is a 2m regulation and a 1m regulation, see the comment on §6 Landesbauordnung NRW. Which one applies to you, I cannot assess without local knowledge, plans, and elevations; according to your description or how I understand you, you are only allowed to fill up 1m without a permit.
However, the fact is that if the neighbor agrees, no building authority will pursue these matters. If the neighbor fills up on their side later, the issue will resolve itself after some time anyway. However, a building encumbrance registration is always a possibility, and I would check that in advance.
If it eventually leads to a building encumbrance registration, €1000 can quickly be gone – just as a rough guideline.
Best regards Dirk Grafe