Add database path logging for sequencer node

[kariy]

No description provided.

[codecov]

Codecov Report

❌ Patch coverage is 66.66667% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 72.58%. Comparing base (9bde0ae) to head (0a4fcbb).
⚠️ Report is 234 commits behind head on main.

Files with missing lines	Patch %	Lines
crates/node/src/lib.rs	66.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #397      +/-   ##
==========================================
- Coverage   73.32%   72.58%   -0.74%     
==========================================
  Files         209      253      +44     
  Lines       23132    29811    +6679     
==========================================
+ Hits        16961    21639    +4678     
- Misses       6171     8172    +2001     

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