Now I feel dumb. But hey, my issue is resolved!
I tried with both of my Siglent devices and indeed, I could telnet into them over port 5025 and issue SCPI commands.
Thanks!
Regarding the project you linked, I did, but I am thinking in a web-based solution, so that I can put a database behind it and save everything by default.
I also have multiple computers that I want to use to look at the logged data.
Since all of my (two) devices can be controlled over ethernet, and I will make this a priority for any new purchase, a web based solution makes the most sense to me.