Align lint fixes with main and resolve merge conflicts

- Convert biome-ignore to oxlint-disable-next-line across client app
- Fix no-base-to-string with type narrowing instead of suppressions
- Fix no-floating-promises with fireAndForget() in proxy app
- Fix restrict-template-expressions with String() wrapping
- Resolve leftover merge conflict markers in manager.rs
- Remove duplicate cmd_plugin_init_errors from lib.rs
- Add graphql as explicit dependency in yaak-client

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/yaak-client/components/core/Hotkey.tsx

@@ -35,7 +35,7 @@ export function HotkeyRaw({ labelParts, className, variant }: HotkeyRawProps) {
       )}
     >
       {labelParts.map((char, index) => (
-        // biome-ignore lint/suspicious/noArrayIndexKey: none
+        // oxlint-disable-next-line react/no-array-index-key
         <div key={index} className="min-w-[1em] text-center">
           {char}
         </div>