Note that this is not as difficult as it sounds. Here is a video explaining how laser cooling works, by using 6 lasers pointing towards a sample with a wavelength just longer than the absorption wavelength of its atoms in order to decrease its momentum regardless of which way it's moving (details near the 2:20 mark):

https://www.youtube.com/watch?v=hFkiMWrA2Bc

So mainstream cryogenics could be a side benefit of technologies like this.

After rereading this, I'm not sure if the ESR itself can perform cooling.

People who design science fiction settings who want people mining the Moon always talk about how we'll need He3 for advanced fusion in the future. But I swear if quantum computing takes off we'll need to mine the moon for He3 for all the dilution refrigerators we'll want to build.

https://en.wikipedia.org/wiki/Dilution_refrigerator

Does that mean at all times (permanently, like whenever the chip is being used) or just during manufacturing?

That "using mostly standard silicon technology" phrase implies that cryogenic temperatures are not needed during manufacturing, only during operation.

'Maintained at / in' usually means continuous or on going.I have not read the paper though, so cannot say for certain.

It means whenever it is being used. Manufacturing silicon chips involves temperatures from room temperature to ~1300C.