interesting as it's working fine on my end and I am also on 3.4.2 on my AGOL account.
is the source of the basemaps from Online directly or via your Enterprise?
Can you provide a screenshot for the source of the layers?
I'm experiencing this exact issue with ArcGIS Pro showing the red exclamation point for basemap vector tile layers.
This only appears if I have the active portal set to my internal ArcGIS Enterprise portal, as setting it to ArcGIS Online the problem goes away. I've also verified that using Pro on a different computer the issue is there as well.
The URL for the Vector Tile Source opens fine in the browser, and I'm not having any issues with loading basemaps from the ArcGIS Enterprise Portal Map application.
This is one of the Vector Tile Services that are being blocked in Pro:
https://cdn.arcgis.com/sharing/rest/content/items/7dc6cea0b1764a1f9af2e679f642f0f5/resources/styles/...
This has resolved itself. No idea what the problem was.