Currently all of the Jakarta EE TCK tests are housed in one big repo and they use a custom test framework from the Java EE days:
It is more convenient to have the TCK tests in the same repo as the API and spec docs because as the technologies change over time all 3 parts (tck/api/spec) can be updated in the same PR. Additionally, implementations can then consume the TCK tests as Maven artifacts and run/verify that they pass the TCK. This is what MicroProfile has done and it works very well.
As an example, I've started this off with the JSON-B TCK test here:
Just wanted to share this with the wider dev community and encourage other specs to follow suit as time permits.