I am not absolutely sure I am building Qwt corectly. I built Qwt thus:
/usr/bin/qmake qwt.pro
make
sudo make install

The strange thing is that all the examples supplied with Qwt works perfectly when build by QtCreator.

The file qwtconfig.pri starts of with:
QWT_VER_MAJ = 6
QWT_VER_MIN = 2
QWT_VER_PAT = 0
QWT_VERSION = $${QWT_VER_MAJ}.$${QWT_VER_MIN}.$${QWT_VER_PAT}
which looks correct to me.

I do not know if it is relevant, but qwt.pro has this information at the start:
lessThan(QT_MAJOR_VERSION, 5) {

lessThan(QT_MINOR_VERSION, 8) {
error(Qt >= 4.8 required.)
}
}

include( qwtconfig.pri )

The version 5 here probably refers to Qt 5.15.3 used by Kubuntu 22.04?
qmake --version
returns
QMake version 3.1
Using Qt version 5.15.3 in /usr/lib/x86_64-linux-gnu

I noticed that there is also qmake6, which returns:
qmake6 --version
QMake version 3.1
Using Qt version 6.2.4 in /usr/lib/x86_64-linux-gnu

So I tried:
make clean
/usr/bin/qmake6 qwt.pro
make
sudo make install
but the problem persists.