The not found is a response from akamai saying you didn't have a file in the address to download. But it does tell us something! It tells us that yes you can reach the akamai servers. Try putting that full path to akamai in your web browser just in case. I suspect it will want to download that small file. If that also works, then it means your computer can reach the patching files, so we know the problem is somewhere else.
I'm running out of things to try, sorry! Some people have used a proxy server with success. You would have to goggle how to do that, there are some free ones. Good luck! I would try skipping any home wifi/router and trying to plug directly into a cable modem/isp modem thing first to see if that makes a difference. And you are absolutely sure that windows defender/any other anti-virus is off, like norton, shield named things from 3rd party companies besides Microsoft, etc, are all turned off, and that anything that mentions anything vaguely similar to "real time protection" is off? I only mention this because often these can "hold" a file downloaded for a few seconds, sometimes timing out any download pending. This is why I also mentioned limiting the download rate in the launcher settings, to avoid any bottlenecks with the download speed overloading anything.