Use a connection pool instead of a single DB connection (#408)

<!-- Provide a brief summary of your changes -->

## Motivation and Context
<!-- Why is this change needed? What problem does it solve? -->
The following PR should fix the recent "conn busy" issue caused by the
PostgreSQL implementation using a single database connection (*pgx.Conn)
instead of a connection pool (*pgxpool.Pool). When multiple concurrent
requests try to access the endpoint, they would conflict trying to use
the same connection.

## How Has This Been Tested?
<!-- Have you tested this in a real application? Which scenarios were
tested? -->
Builds locally

## Breaking Changes
<!-- Will users need to update their code or configurations? -->
No

## Types of changes
<!-- What types of changes does your code introduce? Put an `x` in all
the boxes that apply: -->
- [x] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [ ] Breaking change (fix or feature that would cause existing
functionality to change)
- [ ] Documentation update

## Checklist
<!-- Go over all the following points, and put an `x` in all the boxes
that apply. -->
- [ ] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [ ] My code follows the repository's style guidelines
- [ ] New and existing tests pass locally
- [ ] I have added appropriate error handling
- [ ] I have added or updated documentation as needed

## Additional context
<!-- Add any other context, implementation notes, or design decisions
-->
Related to #400, #405 and #407

---------

Signed-off-by: Radoslav Dimitrov <radoslav@stacklok.com>

go.sum

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