fix: filtering by non-poly relationships with not_equals operator (#7573)

## Description

Fixes #5212

Fixes #6278 

- [x] I have read and understand the
[CONTRIBUTING.md](https://github.com/payloadcms/payload/blob/main/CONTRIBUTING.md)
document in this repository.

## Type of change

- [x] Bug fix (non-breaking change which fixes an issue)

## Checklist:

- [x] I have added tests that prove my fix is effective or that my
feature works
- [x] Existing test suite passes locally with my changes

packages/db-mongodb/src/queries/buildSearchParams.ts

@@ -3,7 +3,7 @@ import type { PathToQuery } from 'payload/database'
 import type { Field } from 'payload/types'
 import type { Operator } from 'payload/types'
 
-import objectID from 'bson-objectid'
+import ObjectIdImport from 'bson-objectid'
 import mongoose from 'mongoose'
 import { getLocalizedPaths } from 'payload/database'
 import { fieldAffectsData } from 'payload/types'
@@ -14,6 +14,8 @@ import type { MongooseAdapter } from '..'
 import { operatorMap } from './operatorMap'
 import { sanitizeQueryValue } from './sanitizeQueryValue'
 
+const ObjectId = ObjectIdImport
+
 type SearchParam = {
   path?: string
   rawQuery?: unknown
@@ -195,16 +197,20 @@ export async function buildSearchParam({
 
       if (field.type === 'relationship' || field.type === 'upload') {
         let hasNumberIDRelation
+        let multiIDCondition = '$or'
+        if (operatorKey === '$ne') multiIDCondition = '$and'
 
         const result = {
           value: {
-            $or: [{ [path]: { [operatorKey]: formattedValue } }],
+            [multiIDCondition]: [{ [path]: { [operatorKey]: formattedValue } }],
           },
         }
 
         if (typeof formattedValue === 'string') {
           if (mongoose.Types.ObjectId.isValid(formattedValue)) {
-            result.value.$or.push({ [path]: { [operatorKey]: objectID(formattedValue) } })
+            result.value[multiIDCondition].push({
+              [path]: { [operatorKey]: ObjectId(formattedValue) },
+            })
           } else {
             ;(Array.isArray(field.relationTo) ? field.relationTo : [field.relationTo]).forEach(
               (relationTo) => {
@@ -225,11 +231,13 @@ export async function buildSearchParam({
             )
 
             if (hasNumberIDRelation)
-              result.value.$or.push({ [path]: { [operatorKey]: parseFloat(formattedValue) } })
+              result.value[multiIDCondition].push({
+                [path]: { [operatorKey]: parseFloat(formattedValue) },
+              })
           }
         }
 
-        if (result.value.$or.length > 1) {
+        if (result.value[multiIDCondition].length > 1) {
           return result
         }
       }