I haven't tested Nextcloud sync with a copy of the web client. However, getting it to work might be similar to the setup for a self-built and hosted copy of Joplin Server.
Enabling access to Joplin Server involves allowing cross-origin access to the web client's domain. Enabling cross-origin access for Nextcloud WebDAV is tracked by this GitHub issue. Owncloud seems to have merged a change that allows users to customize which domains can use its WebDAV API.
For comparison: Joplin Server setup
Joplin Server Setup
With Joplin Server, it's necessary to update the list of domains allowed to connect. In particular, this involves updating corsAllowedDomains:
Adding a new domain to this list should cause the server to add an Access-Control-Allow-Origin: <<origin name here>> header to responses to requests from that domain. This then allows scripts on that domain to receive the response.