We do not recommend Notes syncing with Zimbra at this time (as of 2026).
We only recommend Notes syncing with a single provider, either entirely with Apple (preferred), or Microsoft. So, for clarity's sake, we recommend only syncing Notes with your iCloud account across your devices. We recommend disabling Note syncing on all other services (including our own), so that you don't accidentally create Notes across multiple providers.
The reason for this recommendation is that they each support a different set of Notes features.
Reference Apple Support Knowledgebase article: https://support.apple.com/en-us/118442
In the event you already have Notes synced across multiple providers, or in any event want to transfer Notes between providers, best practice is to copy/paste into new Notes, as other methods, when available, have sometimes been found to deliver inconsistent results.