When linking between dashboards, controls in the destination dashboard do not reflect pinned filters

[GrahamHannington]

Kibana version: 7.12

Selecting a value in a control (say, an "options list" dropdown) in dashboard A creates a filter for the corresponding field; let's call it common_field. That's good.

If you pin that filter, and then click a link (say, in a Markdown panel) to go to dashboard B, the pinned filter persists. Also good.

However, the control on dashboard B for common_field remains empty. That's bad. Ideally, the control should be set to the value of the filter for common_field.

Note: In my use case, dashboard A and dashboard B use different index patterns. Both index patterns contain a string field named common_field.

To reproduce:

1. Create two dashboards, A and B, each with an "options list" control for the same field, common_field. (In my case, the dashboards use different index patterns, but I'm not sure if that's significant; it shouldn't be.)
2. On dashboard A, add a Markdown visualization with a link to the other dashboard (`Dashboard B
3. View dashboard A.
4. Use the control dropdown to set a filter for common_field.
5. Pin the filter.
6. Click the link to go to dashboard B.

On dashboard B, the pinned filter persists (good), but the control dropdown for common_field is empty (bad).

Expected behavior: When I go to a dashboard that has a control that is based on a field for which there is a pinned filter, I expect the control to be populated to match the pinned filter.

Related issue: #101061

[elasticmachine]

Pinging @elastic/kibana-presentation (Team:Presentation)

[ThomThomson]

Closing this in favour of this similar issue for the new Controls system.