Inspired by the chemistry example on p. 15 of the tabularray documentation, you could split the equations into two separate columns and place the `=` in between:

```
\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[left=2.00cm, right=2.00cm, top=2.00cm, bottom=2.00cm]{geometry}
\usepackage{amssymb}
\usepackage{hyperref}
\usepackage{mathtools}
\usepackage{amsthm}
\usepackage{tabularray}
\UseTblrLibrary{diagbox}
\usepackage{siunitx}
\usepackage{ninecolors}
\begin{document}
	\begin{table}[htbp]
		\centering
		\begin{tblr}{
				colspec={lrl},
				column{1}={gray9},
				vlines,
				hline{1,2,Y,Z} = {solid},
				cells={mode=dmath},
        vline{3} = {text=\clap{=}},
			} 
			x  & x_1 & 2 \\
			y & y_{11} & 6
		\end{tblr}
		\caption{}
		\label{tab_01}
	\end{table}
\end{document}
```

![Screenshot 2023-06-15 at 17.31.36.png](/image?hash=afabae57089df91ca415a84a334fbc00877d7a01f49cdeed89eeb21c0e659970)