[tabs] Fix activation direction not updating on programmatic value changes

[Copilot]

• Understand the issue: tabActivationDirection state was not available in the same render cycle for programmatic value changes
• Move tabsListElement state to TabsRoot and expose it via context
• Add synchronous direction computation during render for external value changes
• Simplify TabsList direction calculation for internal clicks
• All 173 Tabs tests pass

Original prompt

Solve mui#3873 by creating a branch in this repo, working on a solution and opening a draft PR against the mui/base-ui repository.
The issue is clear, programatic value updates indeed do not update the activationDirection.
Create tests asserting the behavior is fixed.
You can start by creating the tests, which would fail before working on a solution - TDD approach.

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[LukasTy]

@copilot Recreate this PR in the https://github.com/mui/base-ui repository.

[Copilot]

@copilot Recreate this PR in the https://github.com/mui/base-ui repository.

I'm unable to create PRs in other repositories. I can only work within the repository that's been cloned for me (LukasTy/base-ui). To recreate this PR in the mui/base-ui repository, you would need to:

1. Fork or clone the mui/base-ui repository
2. Apply the same changes from this PR to that repository
3. Open a new PR there

Alternatively, you could open a new issue or PR request in the mui/base-ui repository and have me work on it directly from there.

[LukasTy]

@copilot, I have updated the tests to fail in certain conditions.
They do pass if the click is executed on the tab, instead of click handler updating the state.

Update the solution so it behaves the same regardless of the tab change method.

[Copilot]

@copilot, I have updated the tests to fail in certain conditions.
They do pass if the click is executed on the tab, instead of click handler updating the state.

...

Fixed in ddb7c51. The issue was that external value changes computed the direction in a layout effect after the render, so the panels received the old direction.

The solution moves direction computation to TabsRoot where it's computed synchronously during render for external changes, ensuring the direction is available in the same render cycle as the value change. Internal clicks still calculate direction synchronously before calling onValueChange.

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