Analysis improve

[PenguinWithATie]

• Uses a Store for analysis

• Loads Analysis with a OnceResource and avoids the suspend barrier Use a local resource, no reason no load this in the server. Do a simple refactor for readability but the suspend barrier when providing the context makes sense and should be required (ion is always right :D)

• Ensures uhp strings and the move param in the query can be used in tandem

• Only move in analysis history if arrow is pressed without any modifiers. (Fixes Don't override browser shortcuts in analysis mode #691)

Created the full_path field in Analysis tree

This maintains a full path from root to leaf of a "best guess" for the possible variation the user wants to traverse. Then instead of redrawing everything, jump forward or backward a few moves. It has the following advantages:

• The arrows work fast since a single step is very quick to do.
• Jumping to "near" points in the tree is quick
• In the worst case we need to recompute the full path, which wont happen if the tree isnt to dense. And even then, recomputing the full path for a 150~200 nodes is not that bad.
• Its not required to serialized and can be reconstructed from the rest of the data

Requires #703

Hopefully fixes #508 and #696