Update kitchen-sync example to use react-router v7 in framework mode

[jurgob]

Goals

1. In the kitchen-sync there's an example based on remix. Would it be better to use react-router v7 instead?

I can do the PR if this seems a good idea

Non-goals

1. the blog example and everything else should behave just the same way it is not, this is just a technology update
2. This is a much less ambitious project then this proposal: Proposal: Add name `with-reactrouter-nextjs-storybook` example to showcase full-stack monorepo starter #11427

Background

Seeing remix used there make me feel like the kitchen-sync is not very mantained, so I think using the last version of the react router would make a much better impression

Proposal

I would just foloow this guide: https://reactrouter.com/upgrading/remix

[anthonyshew]

PR welcome!