Naming nitpick: onChanged isn't really a great name for a signal. Usually, "on" is used with slots.

What about connecting Compositing::animationSpeedChanged to Compositing::updateSettings? e.g.

connect(this, &Compositing::animationSpeedChanged,       this, &Compositing::updateSettings);

Given that m_changed is not set to true when anything has been changed, there is a chance that we won't send a reinit request.

We probably need to save the return value of m_settings->isSaveNeeded() before calling m_settings->save() and check it here.

We probably don't need this signal anymore.

Heh, - 4 and + 4 were obscure before so this patch doesn't make things better or worse. Just for context, we add and subtract 4 because long time ago HiddenPreviews had values with different meaning than what we have now. In order to break backwards compatibility, the new values were shifted by 4.

Shouldn't the parent be this?

naming nit: could you please rename these methods to something else? It's unclear what values applyValues applies.

What about these?

void updateSettingsFromUi();
void updateUiFromSettings();

Feel free to ignore this comment because it looks like these methods will go away in D27988