We are going in circles. First thing, formulate what you intend to do? Here is my impression, as an example. Downloading and uploading a (particular 800 MB) file to your Moodle is very slow. You want to find out why, in other words, to find out the weakest link.
Since you connect to your Moodle differently, from the LAN and from the WAN, it is about two things at the same time, which is never good. But the good thing is that you have the tools you need. I have to move on to urgent (and exciting) problems. Good luck! Don't forget to post your findings here. ;)
Hardware and performance
Download and upload speed
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