添加标题以对齐环境

Question

我想为一个方程式创建一个标题，使用对齐环境制作。创建了这个帖子（9 年前）：对齐环境的标题，有人发布了这个解决方案：

\newcounter{captionedequationset} %numbering
\newdimen\captionlength
\newcommand{\captionedequationset}[1]{
    \refstepcounter{captionedequationset}% Step counter
    \setlength{\captionlength}{\widthof{#1}} %
    \addtolength{\captionlength}{\widthof{Equation set~\thecaptionedequationset: }}
    %If the caption is shorter than the line width then
    % the caption is centred, otherwise is flushed left.
    \ifthenelse{\lengthtest{\captionlength < \linewidth }} %
    {\begin{center}
            Equation~\thecaptionedequationset: #1
        \end{center}} 
    { \begin{flushleft} 
        Equation~\thecaptionedequationset: #1 %
        \end{flushleft}}}

我遇到的问题是：

• 标题与公式不对齐。如果出现分页符（如 \clearpage 或普通页面跳转），标题就会与公式分离。
• 计数器不遵循章节号。

这是一个“最小”的 MWE：

\documentclass[12pt]{book}

\usepackage[utf8]{inputenc}

\usepackage{amsmath, lipsum}
\usepackage{calc}
\usepackage{ifthen}

% - - - - - C O M A N D O S - - - - -

% Para poder escribir Caption en ecuaciones matemáticas:
%-- Defines a CAPTION for a set of equations and numbers
%   the set of equations is numbered
% note: the caption adapts the text alignment to the length.
\newcounter{captionedequationset} %numbering
\newdimen\captionlength
\newcommand{\captionedequationset}[1]{
    \refstepcounter{captionedequationset}% Step counter
    \setlength{\captionlength}{\widthof{#1}} %
    \addtolength{\captionlength}{\widthof{Equation set~\thecaptionedequationset: }}
    %If the caption is shorter than the line width then
    % the caption is centred, otherwise is flushed left.
    \ifthenelse{\lengthtest{\captionlength < \linewidth }} %
    {\begin{center}
            Equation~\thecaptionedequationset: #1
    \end{center}} 
    { \begin{flushleft} 
            Equation~\thecaptionedequationset: #1 %
\end{flushleft}}}

% - - - - -  PORTADA - - - - -  

\begin{document}

\chapter{}

\section{Section 1}

The Equation \ref{eq:1} shows an equation.

\begin{align}
    \begin{split}
        \text{Eq 1: }&\\
        & x = 0
    \end{split}
\end{align}
\captionedequationset{Nice equation.\label{eq:1}}

The Equation \ref{eq:2} shows another equation.

\begin{align}
    \begin{split}
        \text{Eq 2: }&\\
        & x^2 = 0
    \end{split}
\end{align}
\captionedequationset{Another nice equation.\label{eq:2}}

\section{Section 2}

The Equation \ref{eq:3} shows another equation.

\begin{align}
    \begin{split}
        \text{Eq 2: }&\\
        & x^2 + x = 0
    \end{split}
\end{align}

\clearpage
\captionedequationset{Another nice equation.\label{eq:3}}

\end{document}

结果如下（忽略出现的 2 和 CHAPTER 1）：

有没有更好的方法来完成此操作？或者，有没有什么方法可以升级此代码并解决问题？