docs: update otlp exporter example to use recommended patterns

[pichlermarc]

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Which problem is this PR solving?

The example has numerous issues that this PR addresses:

• our collector image and config is outdated
• we're using non-recommended patterns in the example, which people may copy and get confused about
• we're not registering shutdown listeners in the example, which causes problems
• we're not really explaining why we're doing the things we're doing, which often leads to questions

I'll gradually update all other examples to a similar pattern too.

Fixes #5602

How Has This Been Tested?

• [x] Manual testing

[codecov[bot]]

Codecov Report

:white_check_mark: All modified and coverable lines are covered by tests. :white_check_mark: Project coverage is 94.95%. Comparing base (4f9b31b) to head (f4322f4). :warning: Report is 180 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #5605   +/-   ##
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  Coverage   94.95%   94.95%           
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  Files         309      309           
  Lines        7946     7946           
  Branches     1608     1608           
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  Hits         7545     7545           
  Misses        401      401           

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