Bluetooth: testlib: `bt_testlib_connect`: better error logs

Changes to logging:
 - Don't log "Connected" if there was an error.
 - Identify the relevant bt_conn object in log messages by its index.
 - Special case non-fatal errors:
  - Failure due to out of free conn object is INF.
 - Improve transparancy of error messages:
  - For errno, include the name of the API.
  - For HCI errors, include the common prefix of the symbols
    'BT_HCI_ERR_' so they are easier to look up.

This change includes some light refactoring to make the code more
understandable, but does not change any behavior.

Signed-off-by: Aleksander Wasaznik <aleksander.wasaznik@nordicsemi.no>