Unify initialization and conversion logic (#3255)

Combine the initialization, implicit conversion, and value category
conversion functions into a single function.

This substantially reduces the duplication between these steps, and
ensures that we support the same set of conversions in all these
contexts. This also fixes some issues where we would not use the proper
value representation for tuples and structs after performing implicit
conversions.

toolchain/check/handle_pattern_binding.cpp

@@ -3,6 +3,7 @@
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
 #include "toolchain/check/context.h"
+#include "toolchain/check/convert.h"
 #include "toolchain/sem_ir/node.h"
 
 namespace Carbon::Check {
@@ -19,7 +20,7 @@ auto HandleGenericPatternBinding(Context& context, Parse::Node parse_node)
 auto HandlePatternBinding(Context& context, Parse::Node parse_node) -> bool {
   auto [type_node, parsed_type_id] =
       context.node_stack().PopExpressionWithParseNode();
-  auto cast_type_id = context.ExpressionAsType(type_node, parsed_type_id);
+  auto cast_type_id = ExpressionAsType(context, type_node, parsed_type_id);
 
   // Get the name.
   auto [name_node, name_id] =