How to download any file to iPad from a cloud drive through the browser?
From my findings, it appears that you simply can't download files with any default free browser.
The most practical way was to use VLC and transfer the file over WiFi from any other device that supports browser file downloads.
Steps that made it work were as follows: (https://techlog360.com/wireless-file-transfer-from-pc-to-ipad-iphone/)

Connect iPad to the same WiFi network as the other device.
Download the file with any other device that supports downloading from a browser.
On the iPad, install VLC.
Open VLC, on the Network settings, turn on &quot;Sharing via WiFi&quot;.
On the device, open the browser and input the IP address that appeared in the step above.
Press the + button, select the files from the device, and upload the files.
The files are then located in &quot;Files (Apple app) -&gt; On My iPad&quot;.