[Dashboard] Add panel flyout opens 2 flyouts

[cchaos]

Kibana version: At least master, but most likely also 7.7 and possibly even earlier

Describe the bug:

There's an EuiFlyout inception that is happening when opening the "Add panel" flyout from Dashboard.

Steps to reproduce:

1. Open or create a new Dashboard
2. Click the "New" button in the menu
3. Watch as you see two levels of flyouts appear during the animation.

Once they're fully open it's hard to tell until you search the rendered dom.

Expected behavior:

One flyout please. The two flyouts can cause the animation to be sluggish and stutter. It will also cause problems with the EUI upgrade that pushes the panel below the header. Nested flyouts will double that amount.

Screenshots (if relevant):

cc @stacey-gammon

[elasticmachine]

Pinging @elastic/kibana-app-arch (Team:AppArch)

[Dosant]

I'll pick it up because had similar issue with drilldowns flyout

[cchaos]

This issue seems to be back. It happens when using the "Replace panel" function in dashboards. Here is a video you can scrub through to see the problem.