Track the evaluation loop outputs in the loop

[carmocca]

What does this PR do?

Follow-up to #10810 and #10923

See comments in code for an overview of the changes

Does your PR introduce any breaking changes? If yes, please list them.

None

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cc @Borda @justusschock @awaelchli @akihironitta @carmocca @edward-io @ananthsub @ninginthecloud

[rohitgr7]

this is great!

[carmocca]

@tchaton this needs your review :)

[tchaton]

Hey @carmocca, some investigation required around add_dataloader_idx=False. I added a test.