chore: Add appmode to debugger analytics (#27242)

## Description

Add `appmode` to debugger analytics

#### PR fixes following issue(s)
Fixes #25730

#### Type of change

- Chore (housekeeping or task changes that don't impact user perception)

## Testing
>
#### How Has This Been Tested?
> Please describe the tests that you ran to verify your changes. Also
list any relevant details for your test configuration.
> Delete anything that is not relevant
- [ ] Manual
- [ ] JUnit
- [ ] Jest
- [ ] Cypress
>
>
#### Test Plan
> Add Testsmith test cases links that relate to this PR
>
>
#### Issues raised during DP testing
> Link issues raised during DP testing for better visiblity and tracking
(copy link from comments dropped on this PR)
>
>
>
## Checklist:
#### Dev activity
- [ ] My code follows the style guidelines of this project
- [ ] I have performed a self-review of my own code
- [ ] I have commented my code, particularly in hard-to-understand areas
- [ ] I have made corresponding changes to the documentation
- [ ] My changes generate no new warnings
- [ ] I have added tests that prove my fix is effective or that my
feature works
- [ ] New and existing unit tests pass locally with my changes
- [ ] PR is being merged under a feature flag


#### QA activity:
- [ ] [Speedbreak
features](https://github.com/appsmithorg/TestSmith/wiki/Guidelines-for-test-plans#speedbreakers-)
have been covered
- [ ] Test plan covers all impacted features and [areas of
interest](https://github.com/appsmithorg/TestSmith/wiki/Guidelines-for-test-plans#areas-of-interest-)
- [ ] Test plan has been peer reviewed by project stakeholders and other
QA members
- [ ] Manually tested functionality on DP
- [ ] We had an implementation alignment call with stakeholders post QA
Round 2
- [ ] Cypress test cases have been added and approved by SDET/manual QA
- [ ] Added `Test Plan Approved` label after Cypress tests were reviewed
- [ ] Added `Test Plan Approved` label after JUnit tests were reviewed

app/client/src/actions/debuggerActions.ts

@@ -2,6 +2,7 @@ import { ReduxActionTypes } from "@appsmith/constants/ReduxActionConstants";
 import type { ENTITY_TYPE, Log, Message } from "entities/AppsmithConsole";
 import type { DebuggerContext } from "reducers/uiReducers/debuggerReducer";
 import type { EventName } from "@appsmith/utils/analyticsUtilTypes";
+import type { APP_MODE } from "entities/App";
 
 export interface LogDebuggerErrorAnalyticsPayload {
   entityName: string;
@@ -15,6 +16,7 @@ export interface LogDebuggerErrorAnalyticsPayload {
   errorType?: Message["type"];
   errorSubType?: Message["subType"];
   analytics?: Log["analytics"];
+  appMode: APP_MODE;
 }
 
 export const debuggerLogInit = (payload: Log[]) => ({

app/client/src/sagas/DebuggerSagas.ts

@@ -399,6 +399,7 @@ function* logDebuggerErrorAnalyticsSaga(
         pageId: currentPageId,
         errorMessage: payload.errorMessage,
         errorType: payload.errorType,
+        appMode: payload.appMode,
       });
     } else if (payload.entityType === ENTITY_TYPE.ACTION) {
       const action: Action | undefined = yield select(
@@ -424,6 +425,7 @@ function* logDebuggerErrorAnalyticsSaga(
         errorMessage: payload.errorMessage,
         errorType: payload.errorType,
         errorSubType: payload.errorSubType,
+        appMode: payload.appMode,
       });
     } else if (payload.entityType === ENTITY_TYPE.JSACTION) {
       const action: JSCollection = yield select(
@@ -441,6 +443,7 @@ function* logDebuggerErrorAnalyticsSaga(
         propertyPath: payload.propertyPath,
         errorMessages: payload.errorMessages,
         pageId: currentPageId,
+        appMode: payload.appMode,
       });
     }
   } catch (e) {