After #2678.

What should be done?

Add operators support to $addFields.

Where?

Supported stages support operators

• $group stage _id expression supports operators
  example: {_id : { $dateToString: { format: "%Y-%m-%d", date: "$date" } } } from manual
  

  FerretDB/internal/handlers/common/aggregations/stages/group.go

  Line 165 in 0992e5f

  groupKey, ok := g.groupExpression.(string)

• $project stage supports operators
  example: {$project: {isbn: {prefix: { $substr: [ "$isbn", 0, 3 ] } } } } from manual
  

  FerretDB/internal/handlers/common/aggregations/stages/projection/projection.go

  Line 361 in 0992e5f

  embeddedSource, err := source.Get(key)

• query projection supports operators
  same example as $project works on projection
  

  FerretDB/internal/handlers/common/projection.go

  Line 371 in 0992e5f

  embeddedSource, err := source.Get(key)

Out of scope

• $match is handled by Support $expr evaluation query operator #414
• $group stage recursive operator is handled by Support recursive aggregation operators #2694

Definition of Done

• all stages updated;
• compatibility tests for every operator in every stage added;
• spot refactorings done;
• find issue number in the code, skipped tests with this issue number passes.