The next generation Starlink (V3) will have 250 square meters of solar panels per satellite, and they are planning on launching about 10,000 of them, so now you're at 2.5 million m^2 of panels or 100 times ISS.
All those satellites have their own radiators to manage heat. True, they lose some heat by beaming it to the ground, but data center satellites would just need proportionally larger radiators.
And, of course, all those satellite have CPUs and memory chips; they are already hardened to resist space radiation (or else they wouldn't function).
Almost every single objection to data centers in space has already been overcome at a smaller scale with Starlink. The only one that might apply is cost: if it's cheaper to build data centers on Earth, then space doesn't make sense (and it won't happen). But prices are always coming down in space, and prices on Earth keep going up (because of environmental restrictions).
But clearly Starlink is not competitive with widely-available residential Internet access offerings, and nowhere near what is expected of terrestrial data centers. People use Starlink when there are no other good options. In the urban areas where most people live, people use land-based ISPs because they are cheaper and better.
An example, by contrast: Trammell Crow is planning a 12 million square foot data center campus in Georgia that will be infinitely more maintainable and have access to better Internet connections than anything space bound. At $8.4B, it will be significantly less expensive than space bound alternatives.
There are better options than space for data centers, so space data centers are unlikely to be a thing. (Someone will probably do a trial for PR though.)