Sorry to hear you’re experiencing trouble with this.
To view ACF Groups on the frontend with Frontend Rendering, the API REST must be enabled.
To do this, either enable the “Show in REST API” setting for the desired ACF Groups or turn off the “Require ACF API REST” option in Cwicly Settings → Advanced Settings.
Note that enabling the REST API for your ACF fields allows any user to query these fields when using Frontend Rendering with Cwicly.
If you prefer to limit access, you can turn ON the “Require ACF API REST” option in Cwicly settings.
Thanks for your report.
Indeed, it seems that ACF fields within ACF Group fields are not retrieved when using the Dynamic Inserter.
When using Dynamic Content directly, ACF fields within ACF Group fields are displayed on the frontend with Frontend Rendering active.