Just a follow-up on this topic:
As I went increasingly frustrated with this - I've decided to quickly test deploy a new single cell from 10.3.2 OVA package (VMware_Cloud_Director-10.3.2.7167-19173640_OVF10.ova).
Prior to deploying it, I've set up the pre-reqs - DNS record, new NFS share, ...
After deploying the cell, I went to do first boot config. The config completed succesfully and it said to access the cell provider on it DNS name. https://test-cell1.lab.local/provider.
However, that again didn't work - again I ended with "Failed to load..." window from the original post. Accessing the provider using IP was of course working fine.
So sadly, even out of the box this doesn't work properly!
I then entered the public address - being the FQDN name of this cell. Note that is still have a single cell for this test. After it, I can access the cell using DNS.
The format of the puiblic record is as follows:
consoleproxy.external.address | test-cell1.lab.local
restapi.baseHttpUri | http://test-cell1.lab.local
restapi.baseUri | https://test-cell1.lab.local
ui.baseHttpUri | http://test-cell1.lab.local
ui.baseUri | https://test-cell1.lab.local
To set these values, you can use the Provider UI -> Administrator -> Public Addresses or cell-management-tool, like in the VMware KB article linked in the first comment.