react with inertia is very bad for seo, even with inertia ssr it won't make that difference to enhanve the SEO , i decided to use next.js (client & server components)
That's completely false. If you use SSR, crawlers have all the necessary data in the initial HTML. They can crawl it without rendering the page in a browser engine, which they typically do in a separate worker queue because it's more resource-intensive.
For small sites, the difference between SSR and CSR is meaningless. For big sites, e.g. an e-commerce site with a million frequently changing product pages, SSR can help with SEO. It's not because crawlers can't index CSR pages (they can) or because the pages are penalized (they're not). It's because parsing HTML has a smaller effect on your crawl budget, which may improve the crawl rate of your site.
How are you going to make Next better from an SEO point of view if you're relying on data retrieved from a Laravel backend? It does you no good if you don't render the (initial) HTML completely server-side. It'll be WORSE than Inertia with SSR. But like I said, it's meaningless for most projects.
Regarding authentication: you can't read HttpOnly cookies in JS, and you don't have to. Cookies are automatically included in every request by the browser. I don't know what you mean by mobile API in this context. You can use sessions on a mobile browser just the same. If you have a separate mobile app that uses an API, you can issue a token after a login from your app, and use that for authentication.