Dependencies tree should appear immediately

(As discussed in: https://github.com/dotnet/roslyn/pull/78778#discussion_r2122383650)

The dependencies tree builds itself using data from both evaluation and design-time builds. The expectation is that it appears immediately after the first evaluation of a project, meaning it should appear populated along with the rest of the tree.

However, while testing another issue, intentionally [delaying design-time builds](https://github.com/dotnet/project-system/blob/main/docs/repo/debugging/design-time-builds.md#delaying-design-time-builds) caused the tree to appear with the same delay, suggesting that the tree is not appearing as early as it should.

Fixing this would improve perceived performance but reducing the number of tree updates. It might also any expansion state in the tree to be restored when a solution is reopened. It'll also reduce the number of tree updates, which are relatively expensive operations in CPS.