fix(web): label ACP page fetches and workspace searches accurately

[incognitojam]

ACP adapters type every search and page fetch as web_search, so in Antigravity threads workspace greps and page fetches all read "Searched web" and counted as web lookups. A turn that grepped the repo five times and fetched three pages showed "9 web lookups". Fetch rows also lost their URL ("Searched web - Fetch URL content"), because the compact activity projection drops ACP's rawInput.

What changed

• Server projection: ACP rawInput now goes through the same allowlisted, length-capped tool-input projection as other providers' input, plus directory_path. The projection runs when activities are read, so existing threads pick this up too.
• Labels (shared, web and mobile): a tool-less web_search row with a URL reads Fetched page - <url>; one with a directory_path reads Searched code - <query>. Real web searches stay Searched web - <query>.
• Claude WebFetch: now reads Fetched page - <url> instead of the tool identifier WebFetch - <url>, so both providers use one name.
• Grouping and counts: ACP workspace searches count as code searches in group summaries ("Searched code 5 times") and as tool calls in the folded-turn header, the same as Claude's Grep, instead of web lookups. On mobile, their rows use the same icon as Grep.
• Thread caches: the web and mobile thread snapshot caches move to a new schema version, as the fork did for command exit codes in fix(web): show command exit codes #11. Otherwise threads already cached on a client would keep the old projection until new activity arrives. I hit exactly this while verifying.

Before and after

The expanded tool group from a real Antigravity turn. The folded header for the same turn went from "6 terminal commands, 9 web lookups" to "6 terminal commands, 4 web lookups, 5 tool calls".

Before	After

Scope and upstream

Upstream fixed read and search classification for its V2 rewrite (pingdotgg#13375), but that isn't on upstream main yet. Its V1 counterpart doesn't apply to the fork cleanly. This change keeps edits to upstream-shared files small: one input source and one allowlisted key in the projection, two classifier conditions, one mobile icon line, and the cache versions. The label logic lives in the fork-only toolRowPresentation.ts. The inspectable-tool-activity ledger entry gains the invariant and tracks that upstream PR for retirement.

This is a follow-up to #580. They touch separate parts of the same files, and the branches merge cleanly together.

Validation

• Compared grouped labels and group categories for 1,352 real work-log entries (Codex, Claude, OpenCode, Antigravity) before and after, running each through the server projection first. 11 changed, all intended: 3 Claude fetches (WebFetch → Fetched page), 3 Antigravity fetches (now with URLs), and 5 Antigravity workspace greps (now Searched code, grouped as code searches). The one real Antigravity web search and all Codex/Claude web searches are unchanged.
• Ran a dev server against a copy of that data and checked the Antigravity thread: the folded header, the group summary, and every row in the expanded group (screenshots above). I fetched the thread snapshot from the server to confirm the projected input carries url and directory_path. I also confirmed the stale header came from the cached client snapshot and cleared after the cache version change.
• Not exercised: Cursor and Grok search payloads. The data had none, so they're only reclassified when they send a directory_path or url. Without either, they keep today's labels. Mobile wasn't opened in a simulator; it shares the presentation code and its tests pass.
• vp test run for the projection, shared presentation, client-runtime presentation, web timeline logic, session logic, mobile thread activity, and web/mobile cache storage; typecheck for server, web, mobile, shared, and client-runtime (mobile's only error is in a pre-existing installed copy of the local markdown module); ledger validation.

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Written by an agent (Claude Code, claude-opus-5-5).