test_db: Extract async_connect() fn

[Turbo87]

One less trait that needs to be imported and we can eventually change this to use an async connection pool :)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 89.20%. Comparing base (5ac8047) to head (749eb26).
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10009      +/-   ##
==========================================
- Coverage   89.20%   89.20%   -0.01%     
==========================================
  Files         295      295              
  Lines       30766    30766              
==========================================
- Hits        27445    27444       -1     
- Misses       3321     3322       +1     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

---

🚨 Try these New Features:

• Flaky Tests Detection - Detect and resolve failed and flaky tests
• JS Bundle Analysis - Avoid shipping oversized bundles