editoast: add 'core' connectivity to the healthcheck

[woshilapin]

We should also check connectivity to the core for the healthcheck.

[codecov-commenter]

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Codecov Report

Attention: Patch coverage is 38.88889% with 22 lines in your changes missing coverage. Please review.

Project coverage is 39.24%. Comparing base (f6e8d72) to head (72929e6).
Report is 5 commits behind head on dev.

Files with missing lines	Patch %	Lines
editoast/src/core/mq_client.rs	0.00%	12 Missing ⚠️
editoast/src/client/mod.rs	0.00%	8 Missing ⚠️
editoast/src/core/mod.rs	66.66%	2 Missing ⚠️

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Additional details and impacted files

@@             Coverage Diff              @@
##                dev    #9393      +/-   ##
============================================
- Coverage     39.25%   39.24%   -0.02%     
  Complexity     2267     2267              
============================================
  Files          1304     1305       +1     
  Lines         98740    98783      +43     
  Branches       3303     3310       +7     
============================================
+ Hits          38763    38767       +4     
- Misses        58023    58055      +32     
- Partials       1954     1961       +7     

Flag	Coverage Δ
core	74.97% <ø> (ø)
editoast	71.95% <38.88%> (-0.07%)	⬇️
front	10.35% <ø> (+<0.01%)	⬆️
gateway	2.50% <ø> (ø)
osrdyne	3.52% <ø> (ø)
railjson_generator	87.49% <ø> (ø)
tests	86.71% <ø> (ø)

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[clarani]

LGTM for the front part ✅

[flomonster]

LGTM (tested)