Compute tree node IDs from UCI instead of relying on server's 'id' field

[Copilot]

The server wants to remove the backward compatibility layer that includes pre-computed 'id' fields in analysis tree nodes.

Changes

• Compute node IDs from UCI: Changed mergeOngoingAnalysis() to derive node IDs using UciCharPair.fromUci(uci) instead of reading node['id']
• Fix incomplete merge: Added recursive merge for newly created branches to process their evaluation data and nested children

Before/After

// Before: relied on server-provided ID
final id = n2child['id'] as String;
final n1child = n1.childById(UciCharPair.fromStringId(id));

// After: compute ID from UCI
final uci = n2child['uci'] as String;
final n1child = n1.childById(UciCharPair.fromUci(uci));

The second fix addresses a pre-existing issue where new variations with nested children would only add the first level - evaluation data and deeper moves were dropped. Now properly recursive.

Original prompt

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This section details on the original issue you should resolve

<issue_title>stop relying on tree node['id']</issue_title> <issue_description>as I would like to remove the BC layer from the server.

The node ID can be computed from the node UCI, it's already happening in the app, somewhere.

I found a use of node['id'] here but there might be others?</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes lichess-org/mobile#2539

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