当坐标轴包含负值时，在axis环境内使用相对坐标出现异常

同样有必要分开两份代码简化你想表述的观点，不然别人看到混在一起的代码很难理解

在描述内容的时候请多为读者着想，下面这些内容也都和你的问题毫无关系，他们理应被删去（也必须被删去）

\usepackage[UTF8]{ctex} % 加载中文支持
\usepackage{bm} % 或 
\usepackage{amsmath}
\usepackage{silence}
\WarningFilter{latexfont}{} % 过滤所有字体警告
\pgfplotsset{compat=1.18} % 版本兼容性设置
\usetikzlibrary{positioning,arrows.meta,angles,quotes,matrix,calc,fillbetween,patterns,patterns.meta,math}
\usepgfplotslibrary{fillbetween}

\usepackage{newtxtext, newtxmath}       % Times 风格字体
\usepackage{bm}                         % 加粗数学符号
\newcommand{\bt}[1]{\bm{\mathit{#1}}}   % 自定义加粗倾斜命令
\newcommand{\axisarrow}
{axis line style = {-{Triangle[length=8pt, width=3pt]}},}   % 修正箭头语法

xlabel = $x$,  
ylabel = $y$,
width=10cm,
height=7cm, 
xlabel style={at={(ticklabel* cs:1)}, anchor=north, below=1pt}, ylabel style={at={(ticklabel* cs:1)}, anchor=east, left=1pt},

问题重述与简化：

第一份代码xmin=-1

\documentclass[tikz,border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis lines = middle,
        xmin = -1, xmax = 5,
        ymin = 0, ymax = 6,
    ]
    \coordinate (O) at (axis cs:1,0);
    \draw[red] (O) --++ (axis cs:0,5);
\end{axis}
    \draw[dashed,blue] (O) --++ (0,5);
\end{tikzpicture}
\end{document}

这将得到：

第二份代码xmin=0:

\documentclass[tikz,border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis lines = middle,
        xmin = 0, xmax = 5,
        ymin = 0, ymax = 6,
    ]
    \coordinate (O) at (axis cs:1,0);
    \draw[red] (O) --++ (axis cs:0,5);
\end{axis}
    \draw[dashed,blue] (O) --++ (0,5);
\end{tikzpicture}
\end{document}

核心点

前后两个代码的坐标系似乎有所差异。其背后的原理探究。

事实上，「当坐标轴包含负值时」并不是问题的关键，看下面的例子：

\documentclass[tikz,border=5pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis lines = middle,
        xmin = 1, xmax = 5,
        ymin = 0, ymax = 6,
    ]
    \coordinate (O) at (axis cs:3,0);
    \draw[red] (O) --++ (axis cs:0,5);
\end{axis}
    \draw[dashed,blue] (O) --++ (0,5);
\end{tikzpicture}
\end{document}

其中xmin=1，效果同样有差异:

meybe related link of the distortion of two coordinate systems of axis and outside tikzpicture.

IMHO, we should do all the drawing concerning with the axis systems inside the axis environment, do them out of the axis will destory the completeness of what axis should do, thus, we should never drawing the vertical dashed line outside the axis in this case, that is exactly, what should be done inside axis environment.

事实上，此事在文档中亦有记载(Page.357)

要想在axis内部使用「相对坐标」，需要使用提供了「direction」信息的axis direction cs,仔细比较下面的例子：

\documentclass[tikz,border=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis lines = middle,
        xmin = -1, xmax = 5,
        ymin = -2, ymax = 6,
    ]
    \coordinate (A) at (axis cs:1,0);
    \coordinate (Delta) at (axis cs:0,3);
    \draw[purple,->,thick] (A) --++ (axis direction cs:0,3);%right
    \draw[blue,->] (A) -- ++(axis cs:0,3);%wrong
\end{axis}
\draw[red,dashed,->,thick] (A) -- ++(0,3);
\draw[blue,dashed,->,ultra thick] (0,0) -- (Delta);
\draw[red,dashed,->,ultra thick] (0,0) -- ++(0,3);
\end{tikzpicture}
\end{document}