[Feature Request]: Add "Move to Schema…" to the object context menu in the Database Projects tree

[aasimkhan30]

Feature Description

Add a "Move to Schema…" context menu (right-click) action on object nodes in the Database Projects tree. Today, Move to Schema is only available from the editor (Refactor… / code action) when a SQL file is open and the cursor is on the object. It would be helpful to also invoke it directly from the project tree by right-clicking an object (table, view, stored procedure, function, etc.) and choosing "Move to Schema…", which would show the same schema picker and refactor preview.

Problem and Motivation

Currently, to move an object to another schema I have to open its .sql file, place the cursor on the object, and use the Refactor menu. When working in the Database Projects tree, it's more natural to act on the object node directly without opening the file first. Adding the action to the tree's right-click menu would:

• Make the feature discoverable where users already manage project objects.
• Save the open-file + position-cursor steps.
• Match the way other object actions are exposed in the tree.

The action should reuse the existing Move to Schema flow (schema picker + refactor preview + refactorlog update), just triggered from the tree node instead of the editor cursor.

Related Area

• SQL Database projects

Confirmation

• I have searched existing feature requests and couldn't find a match
• I want to help implement this feature

[dzsquared]

The current "Move to Schema" functionality does not move the file itself between different schema folders. Not all, but many/most SQL projects are organized by schema/objectType folders.
However, if the "move to schema" functionality is surfaced in the database projects tree, moving the file does become an expectation of that entry point. Can we reliably detect if an object definition file is organized in folders by schema and move the file when appropriate?

edit: ah, was reviewing issues in the reverse order - I see #22385 now

edit 2: we now also can gracefully handle organizing an object's file when moving between schemas, so this functionality (surfacing moving schema from the project tree) would behave as expected and makes sense to add.

[ssreerama]

Moving this to next cycle: related task -> #22709