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Let me illustrate my comment/proposal about continuous refactoring.

1. Step - rebuilding your example - V1

Remember? Start somewhere. Here: rebuilding what you posted for compiles. So it's a useful illustration of the process.

Preparations

I took the liberty to:

• simplify your main.tex a little bit
• put all your files and folders into folder V1 (see screenshot)
• add more versions later, which match the numbers/versions in my Refactoring comment (in the main.tex versions)

You can use a similar versioning approach (copy folder Vn into V(n+1)), use Git etc. Versioning and backup are certainly on your todo- or done-lists.

So, this is what my main.tex looks like in V1, for a simplified start:

% ~~~ REFACTORING ~~~~~~~~~~~~~~~~~~~
%
%  1. getting copies to compile; introducing some formatting
%     activated 1.x and 2.x, dropped bibliography and appendices

\documentclass{report}
\usepackage{geometry}
\usepackage{lipsum}

%\usepackage[backend=biber,style=ieee]{biblatex}
%\addbibresource{bib.bib}

\usepackage[colorlinks]{hyperref}

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\begin{document}
    \input{titlepage/titlepage}
    
    \tableofcontents
    
    \input{1.a/a}
    \input{2.b/b}
    %
    %\printbibliography[heading=bibintoc]
    %\listoffigures
    %\addcontentsline{toc}{chapter}{List of Figures}
    %\listoftables
    %\addcontentsline{toc}{chapter}{List of Tables}
    %
    %\appendix
    %
    %\input{appendix/appendixA}
    %\input{appendix/appendixB}

\end{document}

All needed .tex files are as you posted, within this folder structure:

+- main.tex
+- titlepage/
|   +- titlepage.tex
|- 1.a/
|   +- a.tex
|   +- a1.tex
|   +- a2.tex
|- 2.b/
|   +- b.tex
|   +- b1.tex
|   +- b2.tex

MY first refactoring-action

Preferences, tastes, perception etc. do vary from author to author. For me I'd already perceive your main-code as a bit crowded and hard to tell, what goes where. So I followed my addiction, to put some code-formatting, see above.

Now, after enough compiles, looking ahead, my first attention point was the titlepage-file ... it should be different in my view (still just for demo-purposes).

To emphasize, I line out the way of thinking, the self-improving process, and less the code itself.

2. Step - (first) adjustement of titlepage.tex - V2

Well, in main.tex nothing changed, besides my comment/protocol:

% ~~~ REFACTORING ~~~~~~~~~~~~~~~~~~~
%
%  1. getting copies to compile; introducing some formatting
%     activated 1.x and 2.x, dropped bibliography and appendices
%  2. refactoring titlepage

While in titlepage.tex I took the liberty to

• introduce the titlepage-environement
• add the folder structure (for fanciness) :

\begin{titlepage}
Fancy title:
\vspace{1cm}

    \lipsum[1-2]

\vspace{2cm}

Folders and files used:\bigskip
    \begin{verbatim}
+- main.tex
+- titlepage/
|   +- titlepage.tex
|- 1.a/
|   +- a.tex
|   +- a1.tex
|   +- a2.tex
|- 2.b/
|   +- b.tex
|   +- b1.tex
|   +- b2.tex
    \end{verbatim}
\end{titlepage}

There are millions other ways to design this one ...

3. Step - enabling Chapter 1 to be compiled in two ways:

1. within main.tex
2. separately as a.tex

Required changes in main.tex

% ~~~ REFACTORING ~~~~~~~~~~~~~~~~~~~
% V#  changes
% --- -----------------------------------------------------------
%
%  1. getting copies to compile; introducing some formatting
%     activated 1.x and 2.x, dropped bibliography and appendices
%  2. refactoring titlepage
%  3. adding subfiles to chapter-1 file a.tex, so can be compiled alone

\documentclass{report}
\usepackage{subfiles}   % <<< NEW
\usepackage{geometry}
\usepackage{lipsum}

%\usepackage[backend=biber,style=ieee]{biblatex}
%\addbibresource{bib.bib}

\usepackage[colorlinks]{hyperref}

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\begin{document}
    \input{titlepage/titlepage}
    
    \tableofcontents
    
%   \input{1.a/a}
    \subfile{1.a/a} % <<< CHANGED
    \input{2.b/b}
    %
    %\printbibliography[heading=bibintoc]
    %\listoffigures
    %\addcontentsline{toc}{chapter}{List of Figures}
    %\listoftables
    %\addcontentsline{toc}{chapter}{List of Tables}
    %
    %\appendix
    %
    %\input{appendix/appendixA}
    %\input{appendix/appendixB}

\end{document}

This lets you compile the whole thesis:

Chapter 1 as a pdf

a.tex:

\documentclass[../main]{subfiles}   % <<< new

\begin{document}        % <<< new
    \chapter{First}
    
    \input{1.a/a1}
    \input{1.a/a2}

\end{document}      % <<< new

Compiles into, which might be useful for separate inspection, review, crtics:

4. Process review and outlook

The 3 steps I showed here are already refactoring, like doing pottery on content:

• start simple, with a goal in mind
• gradually transform and check the outcome(s)

Wrt. your thesis I can think of a number of scenarios, like:

• splitting some part of say a.1.tex into more subparts (growing, segmenting)
• consolidating: perhaps later you feel, all b.tex* files should be in one b.tex (growning, merging)
• you recognize, a separate tikz/ folder with standalone drawings is useful
• later you do some finer segmentation on it, like tikz/ch1/, tikz/ch2/ etc.
• and so on

It's all no big deal: you move intentionally and controlled, like a mountain climber, from save-to-save / safe-to-safe :)