Save data table filters in session storage (#20894)

* Save data table filters in session storage

* typing fix

* remove url logic, rename storage key

src/components/ha-filter-entities.ts

@@ -42,6 +42,9 @@ export class HaFilterEntities extends LitElement {
 
     if (!this.hasUpdated) {
       loadVirtualizer();
+      if (this.value?.length) {
+        this._findRelated();
+      }
     }
   }
 
@@ -186,15 +189,12 @@ export class HaFilterEntities extends LitElement {
       return;
     }
 
-    const value: string[] = [];
-
     for (const entityId of this.value) {
-      value.push(entityId);
       if (this.type) {
         relatedPromises.push(findRelated(this.hass, "entity", entityId));
       }
     }
-    this.value = value;
+
     const results = await Promise.all(relatedPromises);
     const items: Set<string> = new Set();
     for (const result of results) {
@@ -204,7 +204,7 @@ export class HaFilterEntities extends LitElement {
     }
 
     fireEvent(this, "data-table-filter-changed", {
-      value,
+      value: this.value,
       items: this.type ? items : undefined,
     });
   }