if username Alex is unique, you can use next code:
db.test.insert({username:"Alex", tags: ['C#', 'Java', 'C++'] });
db.test.aggregate(
{$match: {username : "Alex"}},
{$unwind: "$tags"},
{$project: {count:{$add:1}}},
{$group: {_id: null, number: {$sum: "$count" }}}
);
{ "result" : [ { "_id" : null, "number" : 3 } ], "ok" : 1 }
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