fix(sequentialthinking): restore nextThoughtNeeded in the advertised inputSchema required array

[AmirF194]

Root cause

Commit 1cdf806d (#3533) wrapped nextThoughtNeeded in a z.preprocess()-based coercedBoolean to fix a real footgun (the string "false" coercing to true). zod's toJSONSchema(..., { io: "input" }) treats a z.preprocess()-wrapped field's input type as unknown, so it silently drops that field from the emitted required array, even though the field carries no .optional(). The advertised schema then says nextThoughtNeeded is optional while the runtime validator still requires it, so any client that builds its call arguments from the declared schema gets -32602 Invalid params.

Invariant

The advertised inputSchema.required array and the runtime validator agree on which fields are mandatory for sequentialthinking.

Fix

Rebuild coercedBoolean as a .transform() on an explicit z.union([z.boolean(), z.string()]) instead of z.preprocess(). The union gives toJSONSchema a concrete input type to report, so nextThoughtNeeded stays in required, while parse behavior (including the case-insensitive string coercion #3533 added) is unchanged.

Verification

• Docker (node:22-slim), clean checkout of 76d64c8 (current main): a live stdio MCP session (initialize → tools/list → tools/call) built its call arguments strictly from the advertised required array. Fails on main with MCP error -32602: ... expected boolean, received undefined at nextThoughtNeeded; passes on this branch, and tools/list now reports required: ["thought","nextThoughtNeeded","thoughtNumber","totalThoughts"].
• Same session, sent nextThoughtNeeded: "FALSE" (the case fix(sequential-thinking): use z.coerce for number and boolean params #3533 fixed): still coerces to false on this branch, so the original footgun stays fixed.
• npm run build (tsc) and npm test (vitest, 14/14) both green on this branch.
• What I did not verify: this repo's test suite only covers lib.ts (SequentialThinkingServer), not index.ts (0% coverage before and after this change, per npm test's own coverage report), because index.ts calls runServer() unconditionally at module load, so it isn't imported by the existing tests. I verified the fix with a live protocol session instead of adding a unit test, rather than invent a new import-safe seam (exporting the schema, guarding the runServer() call) that has no precedent anywhere else in this repo's ~30 other reference servers. Happy to add that seam if you'd like a permanent regression test here.

Fixes #4651

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[AmirF194]

#4655 (AbhiPra24, opened 71 minutes after this one) fixes the same nextThoughtNeeded/required drift with the same mechanism (drop z.preprocess for a union that keeps a real Zod type, so toJSONSchema stops dropping the field), plus a broader scope (also fixes #4575's version drift) and a full integration test suite this PR doesn't have. One behavioral difference worth flagging either way: this PR rejects a malformed nextThoughtNeeded string (anything besides "true"/"false") with a validation error, #4655's fallback silently coerces it to false. Happy to stand down in favor of #4655 if that's the one you'd rather take forward.

Update: #4669 (re2zero, opened two days after this one) landed the identical fix, same file, same mechanism, no test suite and no version-drift fix, so it does not change the comparison above.