Who runs it
Google. It names itself with the token Google-InspectionTool, in a mobile and a desktop version.
What it does
It runs the live tests in Search Console, such as URL Inspection and the Rich Results test. Google says it has no effect on Google Search or other products.
Renders JavaScript
Not yet observed. Google's crawler pages don't say whether it runs JavaScript. Search Console shows a screenshot of the rendered page for a live test, and this site hasn't recorded a verified visit yet.
How to verify it
Google lists it among its common crawlers, so the same check applies as for Googlebot. Run a reverse DNS lookup, check the name ends in googlebot.com, then run a forward lookup that returns the same address. Or match the address against Google's published list.
robots.txt
Google lists two tokens for it, Google-InspectionTool and Googlebot, and a rule for either applies. Google says its common crawlers always respect robots.txt rules for automatic crawls.
Questions
Is Google-InspectionTool Googlebot?
No. It has its own user agent token and Google says it has no effect on Google Search.