The oldest CAPI version we support right now is 3.7 (#15839)

Looks like `capi_version < 3.7` is not supported, so I changed the
lowest version to be `3.7`.

Based on the discord discussion.
diff --git a/mypyc/codegen/emitclass.py b/mypyc/codegen/emitclass.py
index 84d19d6..62e1b4b 100644
--- a/mypyc/codegen/emitclass.py
+++ b/mypyc/codegen/emitclass.py
@@ -18,7 +18,7 @@
     generate_richcompare_wrapper,
     generate_set_del_item_wrapper,
 )
-from mypyc.common import BITMAP_BITS, BITMAP_TYPE, NATIVE_PREFIX, PREFIX, REG_PREFIX, use_fastcall
+from mypyc.common import BITMAP_BITS, BITMAP_TYPE, NATIVE_PREFIX, PREFIX, REG_PREFIX
 from mypyc.ir.class_ir import ClassIR, VTableEntries
 from mypyc.ir.func_ir import FUNC_CLASSMETHOD, FUNC_STATICMETHOD, FuncDecl, FuncIR
 from mypyc.ir.rtypes import RTuple, RType, object_rprimitive
@@ -794,11 +794,7 @@
             continue
         emitter.emit_line(f'{{"{fn.name}",')
         emitter.emit_line(f" (PyCFunction){PREFIX}{fn.cname(emitter.names)},")
-        if use_fastcall(emitter.capi_version):
-            flags = ["METH_FASTCALL"]
-        else:
-            flags = ["METH_VARARGS"]
-        flags.append("METH_KEYWORDS")
+        flags = ["METH_FASTCALL", "METH_KEYWORDS"]
         if fn.decl.kind == FUNC_STATICMETHOD:
             flags.append("METH_STATIC")
         elif fn.decl.kind == FUNC_CLASSMETHOD:
diff --git a/mypyc/codegen/emitmodule.py b/mypyc/codegen/emitmodule.py
index f360fab..caf2058 100644
--- a/mypyc/codegen/emitmodule.py
+++ b/mypyc/codegen/emitmodule.py
@@ -43,7 +43,6 @@
     TOP_LEVEL_NAME,
     shared_lib_name,
     short_id_from_name,
-    use_fastcall,
     use_vectorcall,
 )
 from mypyc.errors import Errors
@@ -1107,8 +1106,8 @@
             # We can use vectorcalls (PEP 590) when supported
             return use_vectorcall(capi_version)
         # TODO: Support fastcall for __init__.
-        return use_fastcall(capi_version) and fn.name != "__init__"
-    return use_fastcall(capi_version)
+        return fn.name != "__init__"
+    return True
 
 
 def collect_literals(fn: FuncIR, literals: Literals) -> None:
diff --git a/mypyc/common.py b/mypyc/common.py
index 4615bf3..3d07f6c 100644
--- a/mypyc/common.py
+++ b/mypyc/common.py
@@ -98,11 +98,6 @@
     return name
 
 
-def use_fastcall(capi_version: tuple[int, int]) -> bool:
-    # We can use METH_FASTCALL for faster wrapper functions on Python 3.7+.
-    return capi_version >= (3, 7)
-
-
 def use_vectorcall(capi_version: tuple[int, int]) -> bool:
     # We can use vectorcalls to make calls on Python 3.8+ (PEP 590).
     return capi_version >= (3, 8)
diff --git a/mypyc/test/testutil.py b/mypyc/test/testutil.py
index 796811a..6446af3 100644
--- a/mypyc/test/testutil.py
+++ b/mypyc/test/testutil.py
@@ -102,7 +102,7 @@
 
     # By default generate IR compatible with the earliest supported Python C API.
     # If a test needs more recent API features, this should be overridden.
-    compiler_options = compiler_options or CompilerOptions(capi_version=(3, 5))
+    compiler_options = compiler_options or CompilerOptions(capi_version=(3, 7))
     options = Options()
     options.show_traceback = True
     options.hide_error_codes = True
@@ -272,7 +272,7 @@
         return None
     if "_32bit" in name and not IS_32_BIT_PLATFORM:
         return None
-    options = CompilerOptions(strip_asserts="StripAssert" in name, capi_version=(3, 5))
+    options = CompilerOptions(strip_asserts="StripAssert" in name, capi_version=(3, 7))
     # A suffix like _python3.8 is used to set the target C API version.
     m = re.search(r"_python([3-9]+)_([0-9]+)(_|\b)", name)
     if m: