And I just read the docs on my Siglent instruments, and they all warn that you must ground them through the mains socket grounding terminal.
Only needed if you're working on mains transformers, power supplies and anything that has AC mains going through it. If you're working on Arduinos then ignore it.
Does this actually mean I will very soon electrocute myself?
If it's only a two wire installation then hopefully it has all the required GFIs/RCDs in the distribution box and death is unlikely.
And this room doesn't have polarised mains sockets.
Are any sockets grounded anywhere in the flat? Get a long extension lead from another room.
If not, you could tie the ground to the neutral inside a power strip and plug all your devices into that you
should get the same thing, but ... it could be bad if it goes wrong. You have to make sure your neutral really is neutral. If you do it then be sure to put plenty of "danger" stickers on the power strip and screw it to your table so nobody can borrow it and use it somewhere else. Maybe even put the ground->neutral connection inside a plug which can be removed to make the power strip safe again.
While it is true that the bare metal bits of my lab equipment seem to land at +90 v ac relative to the neutral mains wire, that voltage seems to behind something close to a 100 KOhm.
Measure in amps mode to see if any current flows.
(Wear gloves, ear plugs, dark glasses, don't hold the meter in your hand, etc.
)
Edit: This bit wasn't very serious advice but not everybody will see the part about wearing lots of safety gear as "humor". Don't do this, especially at 90V!
(connect a light bulb between the two instead, see if it glows)