Validated on the combined batch board over tip 8a42aeeb: static gates clean (changelog, file-size 159 frozen, complexity 2621<=2774, cognitive 1181<=1223, dead-code 408<=416), typecheck:core clean, 107 focused tests green.
Zero-credential /v1/search now actually reaches the fallback-only providers (duckduckgo-free/searxng) instead of erroring before the last-resort block could run — the dead-code path is live. Also carries a one-line suppressHydrationWarning on the logo. Thank you @Egorich-print!