Implement $type aggregation operator

[noisersup]

Description

This PR is a first part of this issue. More advanced error handling for recursive calls will be introduce in separate PR to not overcomplicate the review process.

Closes #2678.

Readiness checklist

• I added/updated unit tests.
• I added/updated integration/compatibility tests.
• I added/updated comments and checked rendering.
• I made spot refactorings.
• I updated user documentation.
• I ran task all, and it passed.
• I ensured that PR title is good enough for the changelog.
• (for maintainers only) I set Reviewers (@FerretDB/core), Labels, Project and project's Sprint fields.
• I marked all done items in this checklist.

[codecov]

Codecov Report

Merging #2789 (92f1af2) into main (8ad2489) will increase coverage by 0.10%.
The diff coverage is 74.28%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2789      +/-   ##
==========================================
+ Coverage   63.81%   63.91%   +0.10%     
==========================================
  Files         442      442              
  Lines       22527    22602      +75     
==========================================
+ Hits        14376    14447      +71     
+ Misses       7212     7207       -5     
- Partials      939      948       +9     

Impacted Files	Coverage Δ
...nal/handlers/common/aggregations/operators/type.go	65.57% <64.40%> (+65.57%)	⬆️
...andlers/common/aggregations/operators/operators.go	72.22% <73.91%> (+25.16%)	⬆️
...nternal/handlers/common/aggregations/expression.go	95.45% <100.00%> (-0.05%)	⬇️
.../common/aggregations/operators/accumulators/sum.go	93.40% <100.00%> (+0.38%)	⬆️
...ernal/handlers/common/aggregations/stages/group.go	76.79% <100.00%> (+0.39%)	⬆️
...ommon/aggregations/stages/projection/projection.go	85.60% <100.00%> (+0.53%)	⬆️
...rnal/handlers/common/aggregations/stages/unwind.go	83.00% <100.00%> (+0.52%)	⬆️

Flag	Coverage Δ
integration	56.98% <74.28%> (+0.12%)	⬆️
mongodb	5.01% <0.00%> (-0.02%)	⬇️
pg	56.90% <74.28%> (+0.12%)	⬆️
shard-1	43.84% <70.47%> (+0.51%)	⬆️
shard-2	43.88% <11.42%> (-0.14%)	⬇️
shard-3	42.33% <14.28%> (-0.13%)	⬇️
unit	25.10% <0.00%> (-0.14%)	⬇️

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[rumyantseva]

LGTM!