Moving search `term` into `SearchConfig`

As discussed in the seshat room, it might be useful to move the `term` into the `SearchConfig` and potentially provide a `ConfigBuilder`.

Start by locating the search configuration and the code that currently receives `term`; the issue names `SearchConfig` and a possible `ConfigBuilder` but no files or tests. Done means deciding and implementing how `term` belongs in `SearchConfig`, including whether a builder is needed.

Written by the indexing model from the issue text.