[backport cloud/1.41] test: subgraph integration contracts and expanded Playwright coverage (#10328)

Backport of #10123, #9967, and #9972 to `cloud/1.41`

Includes three cherry-picks in dependency order:
1. #9972 — `fix: resolve all lint warnings` (clean)
2. #9967 — `test: harden subgraph test coverage and remove low-value
tests` (clean)
3. #10123 — `test: subgraph integration contracts and expanded
Playwright coverage` (2 conflicts, auto-resolved by rerere from #10326)

See #10326 for core/1.41 backport with detailed conflict resolution
notes.

---------

Co-authored-by: Amp <amp@ampcode.com>
Co-authored-by: bymyself <cbyrne@comfy.org>
Co-authored-by: GitHub Action <action@github.com>

browser_tests/fixtures/helpers/NodeOperationsHelper.ts

@@ -33,6 +33,7 @@ export class NodeOperationsHelper {
     })
   }
 
+  /** Reads from `window.app.graph` (the root workflow graph). */
   async getNodeCount(): Promise<number> {
     return await this.page.evaluate(() => window.app!.graph.nodes.length)
   }