feat: database module improvements

[germa89]

Description

• Fixing database not using the specified port.
• Removing the context manager for Begin level, and use the standard run_as_routine context manager.
• Relaxing the routines names.
• Refactoring a bit.

Small database module improvements I'm doing while I try to fix the issue #3248

Issue linked

Related #3248

Checklist

• I have visited and read Develop PyMAPDL.
• I have tested my changes locally
• I have added necessary documentation or updated existing documentation.
• I have followed the PyMAPDL coding style guidelines.
• I have added appropriate unit tests that also ensure the minimal coverage criteria.
• I have reviewed my changes before submitting this pull request.
• I have linked the issue or issues that are solved to the PR if any.
• I have assigned this PR to myself.
• I have marked this PR as draft if it is not ready to be reviewed yet.
• I have made sure that the title of my PR follows Commit naming conventions (e.g. feat: adding new MAPDL command)

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[germa89]

Pinging @clatapie for feedback and review.

[germa89]

@pyansys-ci-bot LGTM.

[pyansys-ci-bot]

✅ Approving this PR because germa89 said so in here 😬

[codecov]

Codecov Report

Attention: Patch coverage is 84.31373% with 8 lines in your changes missing coverage. Please review.

Project coverage is 86.21%. Comparing base (93dd176) to head (933d4e7).
Report is 10 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3320      +/-   ##
==========================================
- Coverage   87.13%   86.21%   -0.92%     
==========================================
  Files          55       55              
  Lines        9816    11273    +1457     
==========================================
+ Hits         8553     9719    +1166     
- Misses       1263     1554     +291