doc: revise error.md introduction

PR-URL: https://github.com/nodejs/node/pull/48423
Reviewed-By: Luigi Pinca <luigipinca@gmail.com>
Reviewed-By: Mestery <mestery@protonmail.com>

doc/api/errors.md

@@ -46,15 +46,35 @@ try {
 ```
 
 Any use of the JavaScript `throw` mechanism will raise an exception that
-_must_ be handled using `try…catch` or the Node.js process will exit
+_must_ be handled or the Node.js process will exit immediately.
-immediately.
 
 With few exceptions, _Synchronous_ APIs (any blocking method that does not
-accept a `callback` function, such as [`fs.readFileSync`][]), will use `throw`
+return a {Promise} nor accept a `callback` function, such as
-to report errors.
+[`fs.readFileSync`][]), will use `throw` to report errors.
 
 Errors that occur within _Asynchronous APIs_ may be reported in multiple ways:
 
+* Some asynchronous methods returns a {Promise}, you should always take into
+  account that it might be rejected. See [`--unhandled-rejections`][] flag for
+  how the process will react to an unhandled promise rejection.
+
+  <!-- eslint-disable no-useless-return -->
+
+  ```js
+  const fs = require('fs/promises');
+
+  (async () => {
+    let data;
+    try {
+      data = await fs.readFile('a file that does not exist');
+    } catch (err) {
+      console.error('There was an error reading the file!', err);
+      return;
+    }
+    // Otherwise handle the data
+  })();
+  ```
+
 * Most asynchronous methods that accept a `callback` function will accept an
   `Error` object passed as the first argument to that function. If that first
   argument is not `null` and is an instance of `Error`, then an error occurred
@@ -104,9 +124,9 @@ pass or fail).
 
 For _all_ [`EventEmitter`][] objects, if an `'error'` event handler is not
 provided, the error will be thrown, causing the Node.js process to report an
-uncaught exception and crash unless either: The [`domain`][domains] module is
+uncaught exception and crash unless either: a handler has been registered for
-used appropriately or a handler has been registered for the
+the [`'uncaughtException'`][] event, or the deprecated [`node:domain`][domains]
-[`'uncaughtException'`][] event.
+module is used.
 
 ```js
 const EventEmitter = require('node:events');
@@ -125,60 +145,6 @@ they are thrown _after_ the calling code has already exited.
 Developers must refer to the documentation for each method to determine
 exactly how errors raised by those methods are propagated.
 
-### Error-first callbacks
-
-<!--type=misc-->
-
-Most asynchronous methods exposed by the Node.js core API follow an idiomatic
-pattern referred to as an _error-first callback_. With this pattern, a callback
-function is passed to the method as an argument. When the operation either
-completes or an error is raised, the callback function is called with the
-`Error` object (if any) passed as the first argument. If no error was raised,
-the first argument will be passed as `null`.
-
-```js
-const fs = require('node:fs');
-
-function errorFirstCallback(err, data) {
-  if (err) {
-    console.error('There was an error', err);
-    return;
-  }
-  console.log(data);
-}
-
-fs.readFile('/some/file/that/does-not-exist', errorFirstCallback);
-fs.readFile('/some/file/that/does-exist', errorFirstCallback);
-```
-
-The JavaScript `try…catch` mechanism **cannot** be used to intercept errors
-generated by asynchronous APIs. A common mistake for beginners is to try to
-use `throw` inside an error-first callback:
-
-```js
-// THIS WILL NOT WORK:
-const fs = require('node:fs');
-
-try {
-  fs.readFile('/some/file/that/does-not-exist', (err, data) => {
-    // Mistaken assumption: throwing here...
-    if (err) {
-      throw err;
-    }
-  });
-} catch (err) {
-  // This will not catch the throw!
-  console.error(err);
-}
-```
-
-This will not work because the callback function passed to `fs.readFile()` is
-called asynchronously. By the time the callback has been called, the
-surrounding code, including the `try…catch` block, will have already exited.
-Throwing an error inside the callback **can crash the Node.js process** in most
-cases. If [domains][] are enabled, or a handler has been registered with
-`process.on('uncaughtException')`, such errors can be intercepted.
-
 ## Class: `Error`
 
 <!--type=class-->
@@ -3617,6 +3583,7 @@ The native call from `process.cpuUsage` could not be processed.
 [`--disable-proto=throw`]: cli.md#--disable-protomode
 [`--force-fips`]: cli.md#--force-fips
 [`--no-addons`]: cli.md#--no-addons
+[`--unhandled-rejections`]: cli.md#--unhandled-rejectionsmode
 [`Class: assert.AssertionError`]: assert.md#class-assertassertionerror
 [`ERR_INVALID_ARG_TYPE`]: #err_invalid_arg_type
 [`ERR_MISSING_MESSAGE_PORT_IN_TRANSFER_LIST`]: #err_missing_message_port_in_transfer_list