ObjectSupport plugin issue when loading dayjs in React with script tags

**Describe the bug**
In React, I am loading the ObjectSupport plugin in the browser in the same manner described [here](https://day.js.org/docs/en/plugin/loading-into-browser) by using script tags in the head of `public/index.html`.

Now when I import `dayjs` from `node_modules` to use the library in a component, the ObjectSupport plugin does not work correctly when creating a `dayjs` object like the way described [here](https://day.js.org/docs/en/parse/object). For example, `dayjs` takes this input `dayjs({ year: 2023, month: 7, day: 6, })` and outputs

```
{
$D: NaN
$H: NaN
$L: "en"
$M: NaN
$W: NaN
$d: Invalid Date {}
$m: NaN
$ms: NaN
$s: NaN
$u: undefined
$x: {}
$y: NaN
}
```
However when I remove the import statement `import dayjs from 'dayjs'`, the library and plugin load correctly and output the correct result, albeit a `'dayjs' is not defined` ESLint error is shown when the component is rendered. I could silence the error with `// eslint-disable-next-line no-undef`, but I don't understand why this is happening in the first place.

Am I loading the plugin incorrectly in a React app?

**Expected behavior**
The plugin works correctly when it is imported in head of the HTML file as described [here,](https://day.js.org/docs/en/plugin/loading-into-browser) and also when `dayjs` is imported from `node_modules`.

**Information**
- dayjs: ^1.11.8
- react: ^18.2.0
- react-dom: ^18.2.0
- react-router-dom: ^6.10.0

Start with the script-tag loading example linked in the issue and compare it with the React app's public/index.html and the component's `import dayjs from 'dayjs'`. Reproduce the ObjectSupport call with the reported package versions, then determine whether both loading paths can work together. Done means the object input produces a valid Day.js value when the plugin is loaded from the HTML and Day.js is imported in the component.

Written by the indexing model from the issue text.