You will not damage anything, there should be phase angle correction as part of your cooker. Otherwise you get to run your heating elements for free. This upsets your power company and it also breaks the law.
It basically involves putting a large high voltage large current capable capacitor, of the right value across your load. These have to be non polarised and are likely to cost way more that your SSR.
Finding the right value is not too easy as you generally can’t measure mains with an oscilloscope without a special and costly isolation probe.
You don’t have to correct it to zero, but somewhere around 30 degrees should be enough for your SSR.