Add fair bill splitting tool

Create a standalone Split the Bill Fairly page following the shared tools template and styling conventions. The page is organized into the requested three-card workflow: one card for managing the people involved, one card for entering bill items, and one card for the live per-person totals.

People can be added one at a time and are rendered as removable pills. Removing a person also removes that person from every existing bill item so the item assignments and totals stay consistent.

Each bill item stores an editable name and price, renders participant toggles for every current person, and shows the current per-person share for that item. Newly added items default to all current people selected, while individual participants can be added to or removed from an item with a single click.

Totals are recalculated from the item assignments by splitting each assigned item evenly across the selected people. Items with nobody selected are excluded from per-person totals and called out as unassigned so the visible bill total and distributed total remain understandable.

Add the matching docs markdown file so the tool has a searchable description in the repository metadata after the normal post-commit generation flow.

Verification: node --check on the extracted inline script; git diff --check.

Author: rodrigogiraoserrao

split-the-bill-fairly.docs.md

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+Split a shared bill by adding the people involved, entering each bill item with its price, and selecting who shared each item. The tool calculates every person's total by splitting each item evenly among only the selected people, while showing any unassigned amount when an item has nobody selected.