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You can use the \IfNoValueTF command or its reverse form ( ltnews32 ) to check whether there is an optional argument or not.

\documentclass{article}

\newcommand{\A}[1][]{%
\IfNoValueTF{#1}
{\ensuremath{A_{ab}}}
{\ensuremath{A_{ab,#1}}}
}

\begin{document}
\verb*|$\A$| $\rightarrow\A$

\verb ...

Please create a complete minimal working example and mark its code so that it can be tested using the online compiler.

Read in \newcommand and \renewcommand or an introduction to LaTeX (e.g. learnlatex.org) how to specify the number of arguments when defining a command.

By the way, mathtools loads amsmath.

Please post a link to the topic you started elsewhere so that readers of this topic can find out whether you have already received an answer there.

An example based on yours

\documentclass{article}
\usepackage[many]{tcolorbox}
\usepackage{hyperref}
\usepackage{cleveref}% added

\newtcolorbox[
auto counter,
number within=section,
]{bbb}[2][]{
enhanced,
coltitle=black,
fonttitle=\bfseries,
attach title to upper={\ },
label type ...

Please use the tags intended for multiline code. Apart from a more readable highlighting, it can be tested in the same browser tab without having to copy anything first.

It may not solve the problem, but in the package manual the label is set by an option of the same name.

An environment created ...

Why don't you show us a minimal working example with marked code of what you achieved using the tabularray package manual?

A note: In the first table of section 2.5 "Rows and Columns" you can find out how you can change the height (dimension) of one or more table rows.

You pass the name of a color model as the name of a color. Please read the description of the \color command.

One way to achieve what you want would be

\documentclass[a4paper,12pt]{article}
\usepackage{xcolor}

\ExplSyntaxOn
\NewDocumentEnvironment{that}{O{orange}ommm}
{
#3 #4 #5
\IfValueTF ...

According to the section 3.1.1 "Load-time Options" in the biblatex manual, the package is set to work with biber by default. If you don't need to use the bibtex program run by the editor, then change its setting.

I loaded the package to check if the content of the last column extends into the right margin. Remove or comment out the command that reduces the font size in your example and you'll see what I mean.

kettu_lissa wrote:1) What are those empty rectangles on the right of the table and above it?

See the description of the showframe package I added to the preamble.

kettu_lissa wrote:2) Is there any practical difference between \\ and \par?

Read section 15.1 \par