[Linux/browser] Can I extract a session token/cookie to use with wget or curl?

You can open developer tools, download one of the files, then right click the request in the Network tab and select “Copy as curl command”, this will generate a curl command with all the headers and cookies.

If the token is sent in the header of the request (which is common) then Firefox and Chrome can export the exact request as a curl command from the dev console network tab.

Yes, but you need to install a browser addon first, that allows exporting the cookies as txt files.

https://scrapingant.com/blog/wget-cookies

I know almost nothing about this sort of thing, but I have managed to do what you're describing without an add-on. Go to where you go in the cloud to download. Open your browser console (Ctrl+Shift+C or F12) and go to the Networking tab. Filenames will appear in the Networking tab as you interact with the cloud through the browser. If you right-click on a Filename, a dialogue box for it will open. The first option is Copy Value, which will open a sub-menu that includes Copy as cURL. This option copies everything that your browser sent to the cloud (to get the file you right-clicked) to your clipboard as a cURL command, which you can then paste into a bash script.

This won't work for every cloud provider, but it does for some. Add-ons can be convenient, but there's something to be said for "popping the hood," so to speak. Good luck!

Depending on how they are downloading to your computer you may not have a single URL to download a file, which will increase the effort to do this from curl/wget. Given you are complaining about RAM usage they might have a custom multi-part downloader and assemble the file within the browser's logic. I've seen this on sites like MegaUpload before.