[PT FE] Support any float type for batch norm (#23750)

### Details:
 - *Support any float type for batch norm*
- *Tests for fp16 sporadically fail by accuracy and fp64 is not
supported by torch, will not update tests this time.*

### Tickets:
 - *#23538*

src/frontends/pytorch/src/op/batch_norm.cpp

@@ -36,7 +36,8 @@ Output<Node> broadcast_const_to_channel_dim(const NodeContext& context,
     auto one_i = context.mark_node(v0::Constant::create(element::i32, Shape{}, {1}));
     auto channel_dim = context.mark_node(std::make_shared<v8::Gather>(input_shape, one_i, zero_i));
     auto channel_dim_exp = context.mark_node(std::make_shared<v0::Unsqueeze>(channel_dim, zero_i));
-    return context.mark_node(std::make_shared<v3::Broadcast>(value, channel_dim_exp));
+    auto value_ = context.mark_node(std::make_shared<v1::ConvertLike>(value, input));
+    return context.mark_node(std::make_shared<v3::Broadcast>(value_, channel_dim_exp));
 }
 
 OutputVector make_batch_norm(const NodeContext& context,
@@ -53,10 +54,14 @@ OutputVector make_batch_norm(const NodeContext& context,
     if (!w.get_node_shared_ptr()) {
         auto one_f = context.mark_node(v0::Constant::create(element::f32, Shape{}, {1}));
         w = broadcast_const_to_channel_dim(context, input, one_f);
+    } else {
+        w = context.mark_node(std::make_shared<v1::ConvertLike>(w, input));
     }
     if (!b.get_node_shared_ptr()) {
         auto zero_f = context.mark_node(v0::Constant::create(element::f32, Shape{}, {0}));
         b = broadcast_const_to_channel_dim(context, input, zero_f);
+    } else {
+        b = context.mark_node(std::make_shared<v1::ConvertLike>(b, input));
     }
     auto zero = context.mark_node(v0::Constant::create(element::i32, Shape{}, {0}));
     auto zero_1d = context.mark_node(v0::Constant::create(element::i32, Shape{1}, {0}));
@@ -67,12 +72,16 @@ OutputVector make_batch_norm(const NodeContext& context,
     auto axes = context.mark_node(std::make_shared<v0::Concat>(OutputVector{zero_1d, after_channel_dims}, 0));
     if (!mean.get_node_shared_ptr()) {
         mean = context.mark_node(std::make_shared<v1::ReduceMean>(input, axes, false));
+    } else {
+        mean = context.mark_node(std::make_shared<v1::ConvertLike>(mean, input));
     }
     if (!var.get_node_shared_ptr()) {
         auto current_mean = context.mark_node(std::make_shared<v1::ReduceMean>(input, axes, true));
         auto sub_v = context.mark_node(std::make_shared<v1::Subtract>(input, current_mean));
         auto sqr_sub = context.mark_node(std::make_shared<v1::Multiply>(sub_v, sub_v));
         var = context.mark_node(std::make_shared<v1::ReduceMean>(sqr_sub, axes, false));
+    } else {
+        var = context.mark_node(std::make_shared<v1::ConvertLike>(var, input));
     }
     return {context.mark_node(std::make_shared<v5::BatchNormInference>(input, w, b, mean, var, epsilon))};
 }