There are likely a lot of activity by tugs and barges when this operation is ongoing, but the rig is hardly likely to move about much.
From the picture in post #17 she appears to have 4 anchors installed and deployed.
The normal procedure is to remove the thrusters on arrival, before moving to the yard for whatever major work to be carried out. On completion the rig is towed back to the anchorage to re-install thrusters, before departing Singapore under tow, or under own power. (If loaded out on a HLV the thrusters are usually kept on deck)
Minor work, testing, commissioning and receiving supplies would normally be going on at the same time as thruster installation.
It does appear that she is at anchorage ATTV, which is close to Sembcorp's Mega Yard at Tuas South. Since Jurong West Anchorage was closed, this is the area used for such operations, or for loading/off-loading semi-submersible HLV. (Or anything else involving Rigs)