The Camera is called 'Tianhe Inner Gimbal camera B'
It is a CCTV dome, but it was stowed/uninstalled when first seen.
(This is a partial answer, as it doesn't answer the ISS part)
Seen here before launch:
After the crew enter:
So between arrival on 17 June, and before President Xi Jinping's address to them, the crew do a variety of work, some of which is televised: first night, unpacking, eating, etc.
On the 18th they install WiFI.
This coincides with the appearance of the camera.
Given China's level of technology with this and the implementation of 視覺監控系統 visual surveillance system (https://inf.news/aviation/80b6088cc2b36dc2af2e73e151ddc0db.html)
and the "time-triggered Ethernet spaceborne prototype system" creating a "smart home", these most likely networked IP cameras, would be part of that system of monitoring.
To keep an eye on the well-being of the crew, Tianhe was fitted with an acoustic and optical alarm system to act as an early warning system on the ground for surveillance
In doing this, there is no need for the astronauts to stay awake and be on guard at all times
I have a feeling it might be the package attached to the ceiling next to it seen in early pictures.
The ceiling is a false ceiling, and so whilst the cameras protruded quite far down in previous examples, this one can be seen to be part recessed in the ceiling so it is less in the way.
According to pictures from inside Shenzhou and the earlier Tiangong-1 and 2 stations, they had (smoky) domes with substantial housings.
The televised video shows that it is a PTZ/Gimballed camera that can pan, tilt and zoom.
That camera is labelled as such:
https://www.youtube.com/watch?v=FEkzDXl10XE at 01:35
Other implementations of closed circuit television cameras internally on other craft:
Other cameras are fixed:
2x smaller dome CCTV cameras in node (labelled zenith and capsule direction)
The main cameras televised, showing main interior with control center left and another showing from Node to main interior along sleeping quarters, are labelled the following:
'Tianhe Directional Camera A'
'Tianhe Directional Camera B'
Everything after 23 June shows the dome present, including the most recent footage of the EVA carried out on Sunday 4 July.
The following was just some other idea i was following but it fits this answer too:
on a different note, not related to the dome in the ceiling:
the core cabin of our space station has at least 3 cameras installed on the bulkhead of the camera position, one is used to shoot the scene inside the cabin, that is, the camera we watch live broadcasts, and the other two (or more) are one. Group machine vision system.
It is used for spatial scanning. This is a part of machine vision. After the camera vision calibration is adjusted, a group of cameras or a moving camera can be used to three-dimensionalize the space.
Ground personnel can observe the space station in all directions without blind spots, and can even use VR technology to observe information that cannot be reflected in ordinary two-dimensional monitor photos.
And through processing, the astronaut's motion characteristics will also be presented in a three-dimensional recognizable state.
(coincidentally I have consulted on installing such equipment at installations in the past)
HISTORIC MOMENT when Shenzhou-12 crew enters Tianhe module for the first time
17 Jun 2021
Life of Shenzhou12 astronauts aboard Chinese Space Station
23 Jun 2021
The crew of China's Shenzhou 12 mission salute for a photo inside the Tianhe core module of the Tiangong space station after successfully docking at the module on June 17, 2021. (Image credit: CMSE)
Chinese President Xi Jingping speaks with the three astronauts of China's Shenzhou 12 mission to the Tianhe space station module from the Beijing Aerospace Control Center on June 23, 2021. (Image credit: CMSE)
Chinese astronauts salute as they speak to President Xi Jinping
JUN 23, 2021