Provide more accurate timings for the different test phases

[vkarak]

Now that #1402 is merged, we should have more room to accommodate more frequent status updates and therefore get more accurate timings.

[vkarak]

As discussed in #2531, we use the total time reported in the JUnit report produced by the Gitlab CI integration. The same numbers are used also in the generated report and they don't provide any useful information about the test. We should revise how we generate those.