[json] Increase SerializationBuffer stack size from 512 to 640 bytes

The reduction from 768 to 512 was overly aggressive - the stack
overflow was caused by the 1400+ byte multipart parser, not the
serialization buffer. 640 bytes covers climate DETAIL_ALL payloads
(~520 bytes) on the stack without heap fallback.

esphome/components/json/json_util.cpp

@@ -88,15 +88,15 @@ SerializationBuffer<> JsonBuilder::serialize() {
   //   - Test: objdump -d -C firmware.elf | grep "SerializationBuffer.*SerializationBuffer"
   //     Should show only destructor, NOT move constructor
   //
-  // Try stack buffer first. 512 bytes covers 99.9% of JSON payloads (sensors ~200B,
-  // lights ~170B, climate ~700B). Only entities with 40+ options exceed this.
+  // Try stack buffer first. 640 bytes covers 99.9% of JSON payloads (sensors ~200B,
+  // lights ~170B, climate ~500-700B). Only entities with 40+ options exceed this.
   //
   // IMPORTANT: ArduinoJson's serializeJson() with a bounded buffer returns the actual
   // bytes written (truncated count), NOT the would-be size like snprintf(). When the
   // payload exceeds the buffer, the return value equals the buffer capacity. The heap
   // fallback doubles the buffer size until the payload fits. This avoids instantiating
   // measureJson()'s DummyWriter templates (~736 bytes flash) at the cost of temporarily
-  // over-allocating heap (at most 2x) for the rare payloads that exceed 512 bytes.
+  // over-allocating heap (at most 2x) for the rare payloads that exceed 640 bytes.
   //
   // ===========================================================================================
   constexpr size_t buf_size = SerializationBuffer<>::BUFFER_SIZE;

esphome/components/json/json_util.h

@@ -19,7 +19,7 @@ namespace json {
 /// Buffer for JSON serialization that uses stack allocation for small payloads.
 /// Template parameter STACK_SIZE specifies the stack buffer size (default 512 bytes).
 /// Supports move semantics for efficient return-by-value.
-template<size_t STACK_SIZE = 512> class SerializationBuffer {
+template<size_t STACK_SIZE = 640> class SerializationBuffer {
  public:
   static constexpr size_t BUFFER_SIZE = STACK_SIZE;  ///< Stack buffer size for this instantiation