if you want to distribute your app on linux - don't distribute a binary, deploy to some packaging solution instead (DEB, RPM etc.) - this way the system will make sure that all necessary libs are installed, and it will be done automatically.

Or do a standalone package (AppImage, snap, Flatpak) which will bundle everything inside - then you also don't need to worry about any libs.

However, I have a cmake-based system

The procedure for cmake is the same, only the syntax a bit different:

find_package(QT NAMES Qt6 Qt5 COMPONENTS Core REQUIRED)
find_package(Qt${QT_VERSION_MAJOR} COMPONENTS Core Gui Charts REQUIRED)
# then make sure to link to Charts when building your app
target_link_libraries (yourApp Qt${QT_VERSION_MAJOR}::Charts)

if you want to distribute your app on linux - don't distribute a binary, deploy to some packaging solution instead (DEB, RPM etc.) - this way the system will make sure that all necessary libs are installed, and it will be done automatically.

Or do a standalone package (AppImage, snap, Flatpak) which will bundle everything inside - then you also don't need to worry about any libs.

However, I have a cmake-based system

The procedure for cmake is the same, only the syntax a bit different:

find_package(QT NAMES Qt6 Qt5 COMPONENTS Core REQUIRED)
find_package(Qt${QT_VERSION_MAJOR} COMPONENTS Core Gui Charts REQUIRED)
# then make sure to link to Charts when building your app
target_link_libraries (yourApp Qt${QT_VERSION_MAJOR}::Charts)

How can one verify that the library exists on one's linux box?

Simply check whether the related Ubuntu packages are installed...
Like libqt5charts5-dev which was pointed out in this thread.

The bundled Qt in Ubuntu is not in a single folder, e.g. the header files are in usr/incude/x86_64-linux-gnu/qt5

I have:
// ----------------------------------------------------------------------------------
willem[~]$ dpkg -s libqt5charts5-dev
Package: libqt5charts5-dev
Status: install ok installed
Priority: optional
Section: libdevel
Installed-Size: 286
Maintainer: Ubuntu Developers ubuntu-devel-discuss@lists.ubuntu.com
Architecture: amd64
Multi-Arch: same
Source: qtcharts-opensource-src
Version: 5.12.8-0ubuntu1
Depends: libqt5charts5 (= 5.12.8-0ubuntu1), qtbase5-dev
Description: Qt charts development files
Qt Charts module provides a set of easy to use chart components.
.
This package contains the header development files used for building Qt 5
applications using QtCharts.
Homepage: https://doc.qt.io/qt-5/qtcharts-index.html
Original-Maintainer: Debian Qt/KDE Maintainers debian-qt-kde@lists.debian.org
// -----------------------------------------------------------------------------------
This means the header files are in place. Indeed, I find the header files in usr/incude/x86_64-linux-gnu/qt5

I need away to verify that the correct library is loaded, as opposed to the header file package.

So, I need the library against which these headers can link, typically performed using
QT += charts
in a qmake-based system.

However, I have a cmake-based system.

How can one verify that the library exists on one's linux box?

@sierdzio

I installed the library. However, when I do
#include <QtCharts> in a cpp header file
I get an error "No such file"

You need to add the module in your .pro (or cmake) file:

QT += charts

Since Qt components are not all installed in the same place in the system area, it's not easily possible to upgrade (or even delete) the bundled version. So I am stuck with the bundled Qt.

I don't understand what you mean to say here.

QT += charts

to your pro file as explained in the documentation?

I installed the library. However, when I do
#include <QtCharts> in a cpp header file
I get an error "No such file"

Since Qt components are not all installed in the same place in the system area, it's not easily possible to upgrade (or even delete) the bundled version. So I am stuck with the bundled Qt.

sudo apt install libqt5charts5-dev

Please remember that QtCharts are not available under LGPL license (only GPLv3).

What is the easiest way of getting QtCharts installed on my system?

Use the Qt online installer to install a recent Qt version together with QtCharts (you also will have the maintenance tool then).
Or are you bound to the Qt version Ubuntu is providing?