ENH: Add public LayeredMesh and brain.layered_meshes

[payamsash]

Reference issue (if any)

#13949

What does this implement/fix?

Adds the streaming API discussed in the issue:

• _LayeredMesh changed to LayeredMesh (public, with _LayeredMesh alias kept for compat)
• LayeredMesh.smooth_mat: sparse matrix applied automatically in add_overlay/update_overlay
• Brain.add_data(key="data"): named overlays
• Brain.layered_meshes : access the mesh dict directly
• set_data_smoothing() now syncs smooth_mat onto the mesh
• LayeredMesh exported from mne.viz

Additional information

• "I implemented the code changes myself, and Claude Sonnet 4.6 reviewed it."

[welcome]

Hello! 👋 Thanks for opening your first pull request here! ❤️ We will try to get back to you soon. 🚴

[larsoner]

Oh and I forgot to add... we'll want some updated tests. It looks like some are already failing, see for example

https://github.com/mne-tools/mne-python/actions/runs/27902788239/job/82758652120?pr=13970#step:23:6463

Which suggests you need to make things private or add docstrings. I think map should be private and update public?

Then you'll want to modify an existing test to make use of the basics of the API. I'd take some existing test in test_brain.py that calls add_data and make sure you can access the added LayeredMesh to do what you want -- set some data, and call update. (Modifying an existing test is preferred over making a new test because our existing tests already take ages to run, so piggybacking on some existing ones here is best!)

Typically we also want to showcase this functionality in an updated example... but this is niche enough that I think it's not 100% needed here. You could update something in the Brain example if you were motivated though!

[larsoner]

I'll push the suggestion then merge once the example renders and looks okay. Thanks in advance @payamsash !

[larsoner]

Rendered better this time so marking for merge-when-green, thanks in advance @payamsash !