Migrate to Mantine v9 and Next.js 16

[pfo-omicsstudio]

Mantine v9 requires React's useEffectEvent, which is absent from Next.js 15's bundled React, so Next.js is bumped to 16 as well.

Library (package/):

• Collapse: rename in prop to expanded
• useDataTableColumnToggle, useDataTableColumnReorder: handle useLocalStorage returning undefined in v9; narrow setter types
• DataTableHeaderCell: read columnsToggle from context instead of using function updater with setColumnsToggle

Docs site:

• Grid: rename gutter prop to gap
• Navbar, AppWrapper: adapt to useElementSize/useResizeObserver returning RefCallback instead of RefObject in v9
• InternalLink, PageNavigation, HomePageButtons: add 'use client' (Next.js 16 disallows passing component functions across RSC boundary)
• eslint.config.mjs: drop FlatCompat wrapper (eslint-config-next v16 exports flat config natively)

Dependencies:

• @mantine/* ^8.3.13 → ^9.1.1
• next ^15.5.9 → ^16.2.5
• Peer deps @mantine/core, @mantine/hooks >=8.3 → >=9.0
• mantine-contextmenu kept at ^8.3.13 since there's no v9 release yet

Note: This migration was authored with the assistance of Claude Code.
It is intended to help @icflorescu accelerate the Mantine v9 upgrade.

[pfo-omicsstudio]

Also I extracted HomePageButtons into a client component because Next.js 16 disallows passing component functions like component={Link} across the RSC serialization boundary in server components (in case you were wondering why that change was made)