[Feat]: Support validation of Picker value without rendered child items

### Code of conduct

- [X] I agree to follow this project's code of conduct.

### Impacted component(s)

Picker

### Expected behavior

When user renders a Picker that have already a value set, but the values of the menu-items will be set after initialization - Picker should run some re-comparing and update the current selection state visible in the Picker.

### Actual behavior

When user renders a Picker that have already a value set, but the values of the menu-items will be set after initialization (as this happens sometimes in our project) - the value won't be re-compared to selected value and no selection will be shown in Picker.

### Screenshots

_No response_

### What browsers are you seeing the problem in?

Chrome

### How can we reproduce this issue?

1. Go to https://studio.webcomponents.dev/edit/fFmXO9B4RPvJVzr9Hbp1/src/index.ts?p=stories
2. Compare both Pickers and their current selection

### Sample code that illustrates the problem

_No response_

### Logs taken while reproducing problem

_No response_

Start with the linked reproduction at the webcomponents.dev URL and compare the two Picker instances, especially when menu-item values are assigned after initialization. Trace the Picker selection state during that sequence; done means the existing value is re-compared and the matching selection is visible without initially rendered child items.

Written by the indexing model from the issue text.