docs: refresh developer guides

[nijoe1]

Refreshes developer guide documentation to reflect all synapse packages.

• Update synapse.md to align with current SDK API
• Fix minor inconsistencies across storage/payment docs
• Rewrite react-integration to use @filoz/synapse-react hooks
• Add synapse-core page with @filoz/synapse-core modules usage examples
• Refactor components page with package selection guidance

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Status	Name	Latest Commit	Preview URL	Updated (UTC)
✅ Deployment successful! View logs	synapse-dev	1bb222f	Commit Preview URL Branch Preview URL	Feb 27 2026, 08:24 PM

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[snissn]

Deep-dive review complete. I found and fixed a set of docs API-drift issues in follow-up PR #629 (https://github.com/FilOzone/synapse-sdk/pull/629):\n\n- React guide examples now handle optional wallet address correctly under strict TS settings\n- Storage Context guide examples updated to current options-object download API and valid upload input types\n- Synapse and Synapse Core signatures/examples corrected for current SDK behavior\n\nMergeability status: #628 is CLEAN against master.\n\nRecommendation: once #629 is incorporated into this branch/work (via merge/cherry-pick/rebase), I approve this docs refresh for merge. Without those fixes, I recommend holding merge due to misleading example usage in key developer guides.

[rvagg]

#630 also adds session key docs so it could also be reviewed along with this for fit

[nijoe1]

@hugomrdias @rvagg

All the fixes mentioned above have been applied.

In addition, I've:

• Integrated ts-twoslash into the new SP→toSP storage-operations and storage-contexts pages.
• Added a new "Getting Started" page under Developer Guides to help users choose the right SDK based on their needs.

Suggested follow-ups:
There are a few things I think we should address after this PR most notably, decoupling the storage-contexts page from the split operations page, as storage-contexts has grown quite large and warrants its own dedicated treatment.

I'd recommend we merge this as soon as possible builders are already midway through the 30-day hackathon and need up-to-date docs.

cc: @BigLep