[nextest-runner] use TestInstanceId in more spots

[sunshowers]

Using TestInstanceId makes this code somewhat easier to test.

[codecov]

Codecov Report

Attention: Patch coverage is 55.55556% with 8 lines in your changes missing coverage. Please review.

Project coverage is 80.13%. Comparing base (2dd2644) to head (f2b3009).
Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
nextest-runner/src/reporter/displayer.rs	55.55%	8 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1936   +/-   ##
=======================================
  Coverage   80.13%   80.13%           
=======================================
  Files          82       82           
  Lines       21171    21171           
=======================================
+ Hits        16965    16966    +1     
+ Misses       4206     4205    -1     

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