[sensor] Specialize throttle_with_priority NaN-only case

Short form `- throttle_with_priority: 1s` and explicit `value: nan`
previously generated a `ThrottleWithPriorityFilter<1>` with a lambda
returning NAN stored in a `TemplatableFn<float>` array. Detect this
common case at codegen time and emit a new `ThrottleWithPriorityNanFilter`
that inlines the `std::isnan()` check. Behavior is preserved: NaN
sensor readings still bypass the throttle.

esphome/components/sensor/__init__.py

@@ -275,6 +275,9 @@ ThrottleFilter = sensor_ns.class_("ThrottleFilter", Filter)
 ThrottleWithPriorityFilter = sensor_ns.class_(
     "ThrottleWithPriorityFilter", ValueListFilter
 )
+ThrottleWithPriorityNanFilter = sensor_ns.class_(
+    "ThrottleWithPriorityNanFilter", Filter
+)
 TimeoutFilterBase = sensor_ns.class_("TimeoutFilterBase", Filter, cg.Component)
 TimeoutFilterLast = sensor_ns.class_("TimeoutFilterLast", TimeoutFilterBase)
 TimeoutFilterConfigured = sensor_ns.class_("TimeoutFilterConfigured", TimeoutFilterBase)
@@ -656,9 +659,18 @@ THROTTLE_WITH_PRIORITY_SCHEMA = cv.maybe_simple_value(
     THROTTLE_WITH_PRIORITY_SCHEMA,
 )
 async def throttle_with_priority_filter_to_code(config, filter_id):
-    if not isinstance(config[CONF_VALUE], list):
-        config[CONF_VALUE] = [config[CONF_VALUE]]
-    template_ = [await cg.templatable(x, [], cg.float_) for x in config[CONF_VALUE]]
+    values = config[CONF_VALUE]
+    if not isinstance(values, list):
+        values = [values]
+    # Specialize the common "NaN-only" case (the schema default when the user
+    # omits `value:`) to avoid the TemplatableFn<float> array + NaN lambda the
+    # generic ValueListFilter path requires. Behavior is identical: NaN sensor
+    # readings always bypass the throttle.
+    if all(isinstance(v, float) and math.isnan(v) for v in values):
+        filter_id = filter_id.copy()
+        filter_id.type = ThrottleWithPriorityNanFilter
+        return cg.new_Pvariable(filter_id, config[CONF_TIMEOUT])
+    template_ = [await cg.templatable(x, [], cg.float_) for x in values]
     return cg.new_Pvariable(
         filter_id, cg.TemplateArguments(len(template_)), config[CONF_TIMEOUT], template_
     )

esphome/components/sensor/filter.cpp

@@ -269,6 +269,18 @@ optional<float> throttle_with_priority_new_value(Sensor *parent, float value, co
   return {};
 }
 
+// ThrottleWithPriorityNanFilter
+ThrottleWithPriorityNanFilter::ThrottleWithPriorityNanFilter(uint32_t min_time_between_inputs)
+    : min_time_between_inputs_(min_time_between_inputs) {}
+optional<float> ThrottleWithPriorityNanFilter::new_value(float value) {
+  const uint32_t now = App.get_loop_component_start_time();
+  if (this->last_input_ == 0 || now - this->last_input_ >= this->min_time_between_inputs_ || std::isnan(value)) {
+    this->last_input_ = now;
+    return value;
+  }
+  return {};
+}
+
 // DeltaFilter
 DeltaFilter::DeltaFilter(float min_a0, float min_a1, float max_a0, float max_a1)
     : min_a0_(min_a0), min_a1_(min_a1), max_a0_(max_a0), max_a1_(max_a1) {}

esphome/components/sensor/filter.h

@@ -399,6 +399,19 @@ template<size_t N> class ThrottleWithPriorityFilter : public ValueListFilter<N>
   uint32_t min_time_between_inputs_;
 };
 
+/// Specialization of ThrottleWithPriorityFilter for the common "prioritize NaN"
+/// case: skips the TemplatableFn<float> array + lambda and inlines the check.
+class ThrottleWithPriorityNanFilter : public Filter {
+ public:
+  explicit ThrottleWithPriorityNanFilter(uint32_t min_time_between_inputs);
+
+  optional<float> new_value(float value) override;
+
+ protected:
+  uint32_t last_input_{0};
+  uint32_t min_time_between_inputs_;
+};
+
 // Base class for timeout filters - contains common loop logic
 class TimeoutFilterBase : public Filter, public Component {
  public: