lib/types: update docs to match the new type names

lib/tests/modules/declare-int-between-value.nix

···
+{ lib, ... }:
+
+{
+  options = {
+    value = lib.mkOption {
+      type = lib.types.ints.between (-21) 43;
+    };
+  };
+}

lib/tests/modules/declare-int-unsigned-value.nix

···
+{ lib, ... }:
+
+{
+  options = {
+    value = lib.mkOption {
+      type = lib.types.ints.unsigned;
+    };
+  };
+}

lib/tests/modules/define-value-int-negative.nix

···
+{
+  value = -23;
+}

lib/tests/modules/define-value-int-positive.nix

···
+{
+  value = 42;
+}

nixos/doc/manual/development/option-types.xml

···
   </varlistentry>
 </variablelist>
 
-<para>Integer related types:</para>
+<para>Integer-related types:</para>
 
 <variablelist>
   <varlistentry>
-    <term>
-      <varname>types.ints.signed</varname>
-    </term>
-    <listitem><para>A signed integer.
-    </para></listitem>
+    <term><varname>types.int</varname></term>
+    <listitem><para>A signed integer.</para></listitem>
   </varlistentry>
   <varlistentry>
     <term>
-      <varname>types.ints{signed8, signed16, signed32}</varname>
+      <varname>types.ints.{s8, s16, s32}</varname>
     </term>
     <listitem>
       <para>Signed integers with a fixed length (8, 16 or 32 bits).
···
         </inlineequation>
         respectively (e.g. <literal>−128</literal> to <literal>127</literal>
         for 8 bits).
-    </para></listitem>
-  </varlistentry>
-  <varlistentry>
-    <term><varname>types.int</varname></term>
-    <listitem><para>A convenience alias for <literal>ints.signed</literal>.
     </para></listitem>
   </varlistentry>
   <varlistentry>
     <term>
       <varname>types.ints.unsigned</varname>
     </term>
-    <listitem><para>An unsigned integer (that is ≥ 0).
+    <listitem><para>An unsigned integer (that is >= 0).
     </para></listitem>
   </varlistentry>
   <varlistentry>
     <term>
-      <varname>types.ints{unsigned8, unsigned16, unsigned32}</varname>
+      <varname>types.ints.{u8, u16, u32}</varname>
     </term>
     <listitem>
       <para>Unsigned integers with a fixed length (8, 16 or 32 bits).
···
         for 8 bits).
     </para></listitem>
   </varlistentry>
-  <varlistentry>
-    <term>
-      <varname>types.port</varname>
-    </term>
-    <listitem><para>A network port number (0–65635).</para></listitem>
-  </varlistentry>
 </variablelist>
 
-<para>String related types:</para>
+<para>String-related types:</para>
 
 <variablelist>
   <varlistentry>
···
 
  <section><title>Value Types</title>
 
-   <para>Value types are type that take a value parameter.</para>
+   <para>Value types are types that take a value parameter.</para>
 
 <variablelist>
   <varlistentry>
···
     </term>
     <listitem><para>An integer between <replaceable>lowest</replaceable>
         and <replaceable>highest</replaceable> (both inclusive).
-        Useful for e.g. creating types like <literal>types.port</literal>.
+        Useful for creating types like <literal>types.port</literal>.
     </para></listitem>
   </varlistentry>
   <varlistentry>