Fancy "Side Chapter Thumb Headings"
Here is a suggestion using scrlayer-scrpage. This package uses layers to define page styles. It is possible to define new layers and to add these layers to existing or to new defined layer page styles.
In the following example I declare new layers for the background of the outer margin, the page number, the chapter number and the text in the outer margin. Then I use these layers to define the new pagestyle scth (without the normal header and footer) and they are also added to the default pagestyle scrheadings and to plain.
\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{lipsum}
\usepackage{fourier}
\usepackage{xpatch}
\usepackage[automark]{scrlayer-scrpage}
\renewcommand\chaptermarkformat{}
% define a new mark for the chapter number
\newmarks\chapternum
\xapptocmd\chaptermark{\marks\chapternum{\thechapter}}{}{\PatchFailed}
\newlength\outermarginwidth
\setlength\outermarginwidth{2cm}
\newlength\chapternumbersize
\setlength\chapternumbersize{60pt}
\colorlet{outermarginbgcolor}{lightgray}
\colorlet{outermarginfgcolor}{darkgray}
\newcommand*\outermarginpagemark{%
\ifodd\value{page}\else\hfill\fi%
\tikz[overlay]
\node[circle,fill=outermarginfgcolor,text=white,font=\bfseries,minimum size=6mm]
{\thepage};%
}
\makeatletter
\newcommand\outermarginmark{
\ifodd\value{page}\hfill\else\hspace*{\dimexpr\outermarginwidth*3/8\relax}\fi
\rotatebox{90}{\parbox{\layerheight}{%
\raggedleft
\usekomafont{outermargin}{%
\MakeMarkcase{\ifodd\value{page}\odd@outermargin\else\even@outermargin\fi}}%
}}%
\ifodd\value{page}\hspace*{\dimexpr\outermarginwidth*3/8\relax}\fi%
}
\newcommand*\even@outermargin{}
\newcommand*\odd@outermargin{}
\newcommand*\evenoutermargin[1]{\renewcommand\even@outermargin{#1}}
\newcommand*\oddoutermargin[1]{\renewcommand\odd@outermargin{#1}}
\makeatother
\newkomafont{outermargin}{%
\normalfont\normalcolor
}
\makeatletter
\newcommand*\chapternumbermark{%
\ifodd\value{page}\else\hfill\fi%
\if@mainmatter
{\usekomafont{chapternumber}{\makebox[0pt]{\botmarks\chapternum}}}%
\fi
\vfill
}
\makeatother
\newkomafont{chapternumber}{%
\fontsize{\chapternumbersize}{\chapternumbersize}\selectfont
\color{outermarginfgcolor}%
}
% declare new page style using layers
\DeclareNewPageStyleByLayers{scth}{%
scth.outermargin.bg.even,%
scth.outermargin.bg.odd,%
scth.outermargin.pn.even,%
scth.outermargin.pn.odd,%
scth.outermargin.cn.even,%
scth.outermargin.cn.odd,%
scth.outermargin.text.even,%
scth.outermargin.text.odd%
}
% define the layers for even pages
\DeclareNewLayer[
background,
evenpage,
outermargin,
width=\outermarginwidth,
contents={\color{outermarginbgcolor}\rule{\layerwidth}{\layerheight}}
]{scth.outermargin.bg.even}
\DeclareNewLayer[
foreground,
evenpage,
foot,
hoffset=0pt,
width=\outermarginwidth,
contents=\outermarginpagemark
]{scth.outermargin.pn.even}
\DeclareNewLayer[
foreground,
evenpage,
head,
hoffset=0cm,
width=\outermarginwidth,
align=t,
addvoffset=\dimexpr-\chapternumbersize+\headheight\relax,
height=\chapternumbersize,
contents=\chapternumbermark
]{scth.outermargin.cn.even}
\DeclareNewLayer[
clone=scth.outermargin.cn.even,
addheight=\dimexpr\headheight+\headsep+\textheight\relax,
contents=\outermarginmark
]{scth.outermargin.text.even}
% define the layers for odd page from the settings for even pages
\newcommand*\DeclareOddFromEven[1]{%
\DeclareNewLayer[
clone=#1.even,
oddpage,
align=r,
hoffset=\paperwidth
]{#1.odd}%
}
\DeclareOddFromEven{scth.outermargin.bg}
\DeclareOddFromEven{scth.outermargin.pn}
\DeclareOddFromEven{scth.outermargin.cn}
\DeclareOddFromEven{scth.outermargin.text}
% add the layers to page style scrheadings and page style plain
\ForEachLayerOfPageStyle*{scth}{%
\AddLayersToPageStyle{scrheadings}{#1}%
\AddLayersToPageStyle{plain.scrheadings}{#1}%
}
%----------------------------------------------
% header and footer contents settings
\KOMAoptions{headsepline,markcase=upper}
% for page styles scrheadings and plain
\clearpairofpagestyles
\ohead{\rightmark}
\cfoot{\pagemark}
\ofoot{Authors Name}
% set the contents of the outer margin on even and odd pages for scrheadings, plain and scth
\evenoutermargin{Title of the document}
\oddoutermargin{\leftmark}
\definecolor{lightblue}{RGB}{199,232,250}
\definecolor{darkblue}{RGB}{59,134,215}
\colorlet{outermarginbgcolor}{lightblue}
\colorlet{outermarginfgcolor}{darkblue}
\usepackage{blindtext}
\begin{document}
\frontmatter
\tableofcontents
\mainmatter
\blinddocument
\clearpage
% change some settings
\colorlet{outermarginbgcolor}{orange!30}
\colorlet{outermarginfgcolor}{orange}
\addtokomafont{outermargin}{\color{blue!50!green}}
\evenoutermargin{Changed text on even pages}
\blinddocument
\end{document}
Result:
I tried to adapt the MWE you provided. First I simplified the TikZ code to produce the elements seperately. Then I got stuck with getting the Chapter name displayed. (redefined chaptermark) and assuming, that you only want the thumbs on chapter start pages, I defined the plain style of fancyhdr to produce the style you required. However, a style for right sides is also included, just be sure to display the right text in the border that (the rotate=90-node contains it in the label. Here's a sneak peak (stole the colors fro your image)
by increasing scale= you can enlarge the number and of course you can add like bold face or something, if you want.
And the bottom past of that page looks like
(the blue part is of course at the same place in same width and color) Here's you rewritten MWE:
\documentclass{book}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{lipsum}
\usepackage{xcolor,etoolbox,fancyhdr}
\usepackage{fourier}
\usepackage{titlesec}
\definecolor{lightblue}{RGB}{199,232,250}
\definecolor{darkblue}{RGB}{59,134,215}
\usetikzlibrary{calc}
% Define just chapter start pages
\pagestyle{fancy}
\fancyhf{}\fancyhead[LE,RO]{\sffamily\normalsize\thepage}
\fancyhead[LO]{%\textcolor{mybluei} \rightmark%
\begin{tikzpicture}[overlay,remember picture]
% Box
\draw[fill=lightblue,draw=none] ($(current page.north east) - (1cm,0)$) -- (current page.north east) -- (current page.south east) -- ++ (-1cm,0) -- cycle;
% Chapter Number
\node[scale=3,darkblue] at ($(current page.north east) + (-1cm,-4cm)$) {\thechapter};
% Chapter
\node[rotate=90, anchor=east] at ($(current page.north east) + (-.5cm,-4cm)$) {\leftmark{}};
% Circle for page number
\draw[fill=darkblue,draw=none] ($(current page.south east) + (-1cm,3cm)$) circle (3mm);
% Page number
\node at ($(current page.south east) + (-1cm,3cm)$) {\textcolor{white}\thepage};
\end{tikzpicture}}
\fancyhead[RE]{
\begin{tikzpicture}[overlay,remember picture]
\draw[fill=lightblue,draw=none] ($(current page.north west) + (1cm,0)$) -- (current page.north west) -- (current page.south west) -- ++ (1cm,0) -- cycle;
\node[rotate=90,anchor=east] at ($(current page.north west) + (.5cm,-4cm)$) {\rightmark};
\node[scale=3,darkblue] at ($(current page.north west) + (1cm,-4cm)$) {\thechapter};
\draw[fill=darkblue,draw=none] ($(current page.south west) + (1cm,3cm)$) circle (3mm);
\node at ($(current page.south west) + (1cm,3cm)$) {\textcolor{white}\thepage};
\end{tikzpicture}}
\renewcommand{\chaptermark}[1]{%
\markboth{#1}{}}
\begin{document}
\chapter{My first Chapter: Problems}
\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\subsection{Solution 1}
\lipsum[1-7]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1-4]
\chapter{A second Chapter Title}
\section{Problem 1}
\subsection{Problem 1}
\lipsum[1]
\newpage
\subsection{Solution 1}
\lipsum[1]
\newpage
\section{Problem 2}
\subsection{Problem 2}
\lipsum[1]
\subsection{Solution 2}
\lipsum[1]
\end{document}
Note that the left hand style is commented, the right one isn't but it's the same order just inverted +- and east/west on the x-axis.
Edit For now the chapter style stops in the middle of the chapter number, but that can easily be aligned by changing the corresponding anchors.
Edit #2 Concerning the OPs remarks I notices that the titlesec option was wrong and changed the example to use the general page style fancy.