Hi everybody! this is my first post. I've also been living with this issue for the last couple of months and finally decided to have a look into the problem.
In my case, in addition to not being able to upload files to iCloud Drive via a web browser, I am also unable to save changes in my iCloud Notes from a web browser.
As far as I can tell, this is a simple DNS issue which could easily be solved by Apple. You can work around the issue by creating a local hosts file entry so that your web browser can find the IP of an application server which Apple mysteriously removed DNS entries for.
Step 1) Determine which domain name is failing in your case
- Log in to iCloud in a web browser, open dev tools (press f12 to open dev tools in Chrome)
- Navigate to the "Network" tab in dev tools
- Attempt to upload a file to iCloud
- Click on one of the "singleFileUpload" items in the network log
- Take note of the domain name in the Request URL. In my case the domain name is "p30-contentws.icloud.com" yours will probably be the same name but with a different number at the beginning.

Step 2) Find a suitable IP address to use
- open a command prompt/terminal window and run the following command:
- nslookup contentws.icloud.com
- Take note of any IP address in the list of addresses returned for "contentws.icloud.com"

Step 3) Create a local host file entry for the missing domain name
- Run notepad.exe as administrator then open "c:\windows\system32\drivers\etc\hosts"
- add the following entry to the bottom of the file:
- 17.178.100.27 p30-contentws.icloud.com
- replace "p30-contentws.icloud.com" with the domain name you found in Step 1
- replace "17.178.100.27" with the IP address you chose in Step 2
- Save the hosts file.

- Refresh icloud.com.
- upload files successfully.

Various Notes
- These instructions are written using Chrome on Windows 10 but the same can be achieved with any browser/OS if you know how to operate your computer.
- I'm not a mac user, but I know your hosts file is located at "/etc/hosts". Google "how to edit hosts file on mac" for more details.
- It looks like Apple uses Akamai GTM for DNS load balancing, every time you do an nslookup you get a different list of IPs. Apple probably relies on this technology to update their applications without downtime so it's possible that at some point in time the IP you choose will be offline.
- credit to Hanadark0 for recognizing there was a DNS problem on 12/14/21 (35 days ago). Seriously Apple. Please fix this.