Hidden Streets Streetss between boundaries can be invisible to queries

How to include the boundary roads in a query for roads within a town?

A suburb called Beaconsfield (NSW, Australia) is bounded by six streets and three other suburbs.
The following query lists a total of nine streets in the Beaconsfield suburb,

[bbox:-33.9142158, 151.1919887, -33.9066269, 151.2080568];

Visual inspection of the map confirms the presence of the nine streets in Beaconsfield and also six streets around the boundary.

None of the bounding streets are included in the script results list.

Similar queries of the adjoining suburbs demonstrate that five of the six boundary streets are not included in similar lists of streets for those suburbs either. The one exception occurs because that street, William Street, projects beyond a boundary into the adjoining suburb of Alexandria.

Some of the boundary streets (by not extending beyond the suburbs) would never be detected by scripts such as that above.

How can such boundary streets be readily listed?
Preferably - included in the list of results of streets within the suburb boundary?