Only call SpanProcessor onStart / onEnd if required

[jack-berg]

Fixes #5930.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (17b8f43) 90.95% compared to head (4ffe274) 90.94%.

Additional details and impacted files

@@             Coverage Diff              @@
##               main    #6112      +/-   ##
============================================
- Coverage     90.95%   90.94%   -0.01%     
- Complexity     5682     5683       +1     
============================================
  Files           628      628              
  Lines         16672    16674       +2     
  Branches       1651     1653       +2     
============================================
+ Hits          15164    15165       +1     
  Misses         1051     1051              
- Partials        457      458       +1     

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