agent: Add Burn Mode setting migrator (#31718)

Follow-up https://github.com/zed-industries/zed/pull/31470.

Release Notes:

- N/A

crates/migrator/src/migrations/m_2025_05_29/settings.rs

@@ -0,0 +1,51 @@
+use std::ops::Range;
+use tree_sitter::{Query, QueryMatch};
+
+use crate::MigrationPatterns;
+use crate::patterns::SETTINGS_NESTED_KEY_VALUE_PATTERN;
+
+pub const SETTINGS_PATTERNS: MigrationPatterns = &[(
+    SETTINGS_NESTED_KEY_VALUE_PATTERN,
+    replace_preferred_completion_mode_value,
+)];
+
+fn replace_preferred_completion_mode_value(
+    contents: &str,
+    mat: &QueryMatch,
+    query: &Query,
+) -> Option<(Range<usize>, String)> {
+    let parent_object_capture_ix = query.capture_index_for_name("parent_key")?;
+    let parent_object_range = mat
+        .nodes_for_capture_index(parent_object_capture_ix)
+        .next()?
+        .byte_range();
+    let parent_object_name = contents.get(parent_object_range.clone())?;
+
+    if parent_object_name != "agent" {
+        return None;
+    }
+
+    let setting_name_capture_ix = query.capture_index_for_name("setting_name")?;
+    let setting_name_range = mat
+        .nodes_for_capture_index(setting_name_capture_ix)
+        .next()?
+        .byte_range();
+    let setting_name = contents.get(setting_name_range.clone())?;
+
+    if setting_name != "preferred_completion_mode" {
+        return None;
+    }
+
+    let value_capture_ix = query.capture_index_for_name("setting_value")?;
+    let value_range = mat
+        .nodes_for_capture_index(value_capture_ix)
+        .next()?
+        .byte_range();
+    let value = contents.get(value_range.clone())?;
+
+    if value.trim() == "\"max\"" {
+        Some((value_range, "\"burn\"".to_string()))
+    } else {
+        None
+    }
+}