Fix to work RECHECK_SYNC_BACKEND correctly

[makenowjust]

Close #870

Changes

• Fix to work RECHECK_SYNC_BACKEND correctly
  • A break for switch-case is missing. It is easy mistake.
• Add a test case for checking whether synckit function has been called.

[codecov-commenter]

Codecov Report

Merging #872 (3cd1173) into main (4c51c22) will decrease coverage by 1.70%.
The diff coverage is 100.00%.

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@@            Coverage Diff             @@
##             main     #872      +/-   ##
==========================================
- Coverage   99.05%   97.35%   -1.70%     
==========================================
  Files          69       13      -56     
  Lines        3066     1098    -1968     
  Branches      537      180     -357     
==========================================
- Hits         3037     1069    -1968     
  Misses         29       29              

Impacted Files	Coverage Δ
packages/recheck/src/main.ts	100.00% <100.00%> (ø)

... and 56 files with indirect coverage changes

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