convex-backend PR 62: (docs) update /clerk guide (#36729)

Clerk employee here 👋 While updating the Clerk docs' Convex integration guide [(PR)](clerk/clerk-docs#2119), I noticed this guide could use some love. From the Clerk Docs team to yours 💜

Notes about the changes:
- The Tanstack Start link 404'd, so I updated it, but you'll see that it's moved farther down the page into a `Tanstack Start` section. This may get moved to the top again pending on your feedback about this next point:
- I've added a `Next.js` section, which bloats the page, and I think could get moved to https://docs.convex.dev/client/react/nextjs/with-clerk similar to how you do it for [Tanstack Start](https://docs.convex.dev/client/react/tanstack-start/tanstack-start-with-clerk). Let me know what you think and I can update the PR because I have an idea of how to reorganize this guide once that `Next.js` section is moved.
- Updated the steps thoroughly.
- Removed "Login and logout Flows" and combined it with "Logged-in and logged-out views". Ensured that this section is available in both the `React` and `Next.js` sections. I removed them as "supplemental" (at the bottom of the guide) sections because they are already included in the React/Next.js set ups, and its repetitive information. Plus, the guide now mentions to users to use the `React` setup guide if their guide isn't listed. So if they're using Expo, or any other React-based SDK, this information is still available on the page for them.
- Removed "Next.js, React Native Expo, Gatsby" in favor of the new addition at the top of the guide (the first paragraphs under "Getting started"). Now when a user hits the page, and they say "wait this is for React, what about my SDK?" They are immediately presented with information about what to do if their SDK isn't listed.
- Rewrote "Configuring a React client" to "Configuring Clerk's API keys" as that seems to be the purpose of the section - configuring Clerk's keys in dev vs. prod instances. Updated the copy here to be more clear about the intended purpose of the section.

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Co-authored-by: Alexis Aguilar <[email protected]>
GitOrigin-RevId: 7d0a4d77322ce143ed8af1712b0306a3efa3e36c

Author: 2 people