fix(color-picker): fix error caused by initial value with a different…

… format (#11351)

**Related Issue:** #10731  

## Summary  

Adds missing check to skip internal, equal values after transitioning to
getters/setters in #10310.

packages/calcite-components/src/components/color-picker/color-picker.e2e.ts

@@ -2470,4 +2470,14 @@ describe("calcite-color-picker", () => {
       });
     });
   });
+
+  it("does not throw when initialized with different format value (format='auto')", async () => {
+    async function doTest(): Promise<void> {
+      const page = await newE2EPage();
+      await page.setContent(`<calcite-color-picker value="rgb(89, 77, 77)"></calcite-color-picker>`);
+      await page.waitForChanges();
+    }
+
+    await expect(doTest()).resolves.toBeUndefined();
+  });
 });

packages/calcite-components/src/components/color-picker/color-picker.tsx

@@ -549,7 +549,8 @@ export class ColorPicker extends LitElement implements InteractiveComponent, Loa
     if (modeChanged || colorChanged) {
       this.internalColorSet(
         color,
-        this.alphaChannel && !(this.mode.endsWith("a") || this.mode.endsWith("a-css")),
+        (this.alphaChannel && !(this.mode.endsWith("a") || this.mode.endsWith("a-css"))) ||
+          this.internalColorUpdateContext === "internal",
         "internal",
       );
     }