Partial answer to a different but very related question:
(What exactly is this device? What is it's function, how does it work? Is it basically the keys to Nauka's front door? When did it get to the ISS? from @uhoh)
From the same link in the answer above i got most of the answers below:
What is it's function,
allows you to unlock, open and then remove the hatch.
how does it work?
Lots of gears. Not found a technical description or pictures.
(if i find it i'll update this..)
Is it basically the keys to Nauka's front door?
Also keys to Progress, Soyuz, FGB, SM and PMA-1 doors...
When did it get to the ISS?
It is part of a docking accessories kit that includes wipes, extension tool and hatch cover. One kit went up on 2 November 2000 with first crew, unsure if it returned on the decent module though.
It would have been required then to open the hatch to enter Zvezda SM, Zarya FGB and their side of PMA-1.
After all the hatch openings it was returned to a docking accessories kit which was stored inside Soyuz.
So, my understanding is that each Soyuz has one, as they refer to a 'nominal position' it is kept in.
The others were launched with each module:
An identical kit is in a storage position on the axial transfer section on Zvezda.
(https://blogs.nasa.gov/stationreport/2020/11/20/iss-daily-summary-report-11-20-2020/ says: "Checking Docking Assembly (СтА) accessories kit stowage in SM ПрК" which is Zvezda's rear transfer tunnel)
Another kit is in storage location on panel 230 in FGB.
And another kit was tethered.to PMA-1 hatch handle, and later got moved to Unity module.
Nauka MLM probably has one so they do not need to keep going into the other modules to get parts from those kit bags.