docs(core-client): HeaderPill's page effects live in header-effects since #803 #837

docs/subsystems/core-client.md still says the pill owns three page effects that #803 moved out of it. HeaderPill no longer runs them: installHeaderEffects (core/src/client/header-effects.js), installed once from apply, owns each one under its own key. The paragraphs in the doc were only partly updated when #803 landed, so a reader is told to look in header.js for code that is in header-effects.js.

The four statements that are now wrong (main 7c1a5fcb)

• docs/subsystems/core-client.md:99 — "HeaderPill holds the localized Message {name} label … in a layout effect" and, in the same bullet, "In a friend's Bot chat it also sets body[data-bt-friend-chat]". Both are installHeaderEffects keys now: composer-label (header-effects.js:65, holdComposerLabel) and friend-chat (:48).
• docs/subsystems/core-client.md:108 — "An empty chat with a friend's Bot shows a one-line hint (--bt-remote-empty, set by HeaderPill)". It is set by the remote-empty key in installHeaderEffects (header-effects.js:55-61).
• docs/subsystems/core-client.md:171 — "HeaderPill (header.js) starts actions.filterFaceAtMenu for a face room". It is the face-at-menu key in installHeaderEffects (header-effects.js:74-76).

What is still true, and must stay: docs/subsystems/core-client.md:98 — "Only --bt-first-sep still rides the pill" — matches header.js:63-65, the only body-level write left in that file. :97 and :98 already name installHeaderEffects correctly.

Acceptance criteria

• The four statements above name installHeaderEffects (src/client/header-effects.js) instead of HeaderPill / header.js, each keeping its current issue references (Social UI polish: friend settings shell, approval affordances, face-room copy (aesthetics/usability) #166, Friend's Bot chat on the receiving home: 'Tool removed' line, turns/steps/tok/s footer, composer placeholder flips to coding copy #419, Invite and friend-chat polish: coding-agent placeholder in a friend's Bot chat (regression of #419), two inconsistent invite UIs, Add friend leftovers, Sharing hint #499, Face room @ picker lists a friend's Bot 5 times in 3 sections, 'Everyone · 1 members'; mention chip renders differently per home; Bot named 4 ways #305).
• The remaining HeaderPill mentions in this file are only the ones that are still true: the pill's mount point (:96), test/header-slot.test.js pinning that no such effect runs in it (:97), and --bt-first-sep (:98). No other wording changes.
• The change edits docs/subsystems/core-client.md only — no core/ code, no tests. changelog check and testing-layers --check pass; arch-docs needs no trailer because no owned source file changes.
• A grep for set by HeaderPill, HeaderPill (header.js) and HeaderPill holds in this file returns nothing.

Refs #803 (moved the effects), #820 (the header seat that replaced the old corner registration).