Conditional grouping with $exists inside $cond

Use $ifNull instead of $cond in your $project:

{ $project: {MyKey: {$ifNull: ['$A', '$B'] }}}

If A exists and is not null its value will be used; otherwise the value of B is used.

if one wants to check $exists with in $cond an alternative approach is to use $not with $cond

{$project: {MyKey: {$cond: [{$not: ["$A"]}, "$B", "$A"]}}}

and truth table for $not is as

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