I couldn't find any known issues with SvelteKit and sessionStorage on Opera GX. However, there are a few things you could check to resolve the "access denied" error:

Make sure you are accessing sessionStorage within a browser context (i.e. not in a Node.js environment).

Ensure that the browser settings on Opera GX are allowing sessionStorage to be used. You can check this by going to the browser settings -> privacy and security -> site settings -> cookies and site data -> allow sites to save and read cookie data.

Try clearing your browser cache and cookies, then restart the browser and try again.

If the issue persists, try using a different storage mechanism such as localStorage, which may work for your use case.
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