Support schema selection through PgBouncer without startup `options`

When a schema is selected in a connection profile, the extension passes it
through the PostgreSQL startup option:

options=-c search_path=public,client_schema

Some PgBouncer configurations reject this with:

FATAL: unsupported startup parameter in options: search_path

A connection without options succeeds, but schema-aware queries cannot be
used through such PgBouncer endpoints.

Please consider adding an optional connection-initialization SQL command, for
example:

SET search_path TO public, client_schema;

Manually prepending SET search_path TO public, client_schema; to every query is not an
equivalent workaround. It does not provide schema context to extension
features such as IntelliSense, which can then suggest a large number of
objects from unrelated schemas. It also makes query-history entries less
useful, since many queries begin with the same SET search_path TO public, client_schema; statement.

Start by tracing how the extension handles schema selection in connection profiles and constructs PostgreSQL startup options. Find the connection-initialization path and determine how an optional SQL command could run before schema-aware features; done means schema selection works through PgBouncer without embedding SET statements in every query.