I have made an example that calls emscripten_request_pointerlock("document", false); by mouse click:

void mousePressEvent(QMouseEvent *event) override
{
    EMSCRIPTEN_RESULT result = emscripten_request_pointerlock("document", false);
    qDebug() << result;
}

It print -4 to the console that means EMSCRIPTEN_RESULT_UNKNOWN_TARGET

main.cpp

#include <QtGui/QMouseEvent>
#include <QtGui/QOpenGLFunctions>
#include <QtOpenGL/QOpenGLWindow>
#include <QtWidgets/QApplication>

#ifdef Q_OS_WASM
#include <emscripten.h>
#include <emscripten/html5.h>
#endif

class OpenGLWindow : public QOpenGLWindow, private QOpenGLFunctions
{

public:

    OpenGLWindow()
    {
        setTitle("OpenGL ES 2.0, Qt6, C++");
        resize(350, 350);
    }

private:

    void mousePressEvent(QMouseEvent *event) override
    {
        EMSCRIPTEN_RESULT result = emscripten_request_pointerlock("document", false);
        qDebug() << result;
    }

    virtual void initializeGL() override
    {
        initializeOpenGLFunctions();
        glClearColor(0.2f, 0.2f, 0.2f, 1.f);
    }

    virtual void paintGL() override
    {
        glClear(GL_COLOR_BUFFER_BIT);
    }
};

int main(int argc, char *argv[])
{
    QApplication::setAttribute(Qt::ApplicationAttribute::AA_UseDesktopOpenGL);
    QApplication app(argc, argv);
    OpenGLWindow w;
    w.show();
    return app.exec();
}

pro

QT += core gui openglwidgets

win32: LIBS += -lopengl32

CONFIG += c++17

wasm: INCLUDEPATH += "C:emsdkupstreamemscriptencachesysrootinclude"

SOURCES += 
    main.cpp