Restrict default search view for logged-in users to eligible studies

# TL;DR

Rather than users actively selecting from a drop-down to see studies for Child1 or Child2, can we have the default to show studies they are eligible for? On the UI side, this might look like 'tag' filters that can be added/removed by the family:

Default tags:

x[Child 1] x[Child 2] x[Child 3]

Where you can click X to remove a tag. If no child has been selected, then show all studies.

# Narrative

As a family, I want to encounter studies I can actually take when I click on them. When I'm logged in, the first study I click on I may not be eligible for, because I'm shown all the listed studies.

# Acceptance Criteria

- Make sure that child/tag selection interacts appropriately with the other filters! (Studies we've already done, studies on/off lookit, tabs for external/internal studies)

No files or tests are named. Start by tracing the default study search view and its existing child, tag, completion-status, Lookit, and internal/external study filters. Done means logged-in families see eligible studies by default, can remove or restore child selections, and all other filters continue to interact correctly.

Written by the indexing model from the issue text.