It looks like the issue is with the path to the CSS file. Try changing the import statement in your app.css file to:
@import '~tom-select/dist/css/tom-select.default.css';
The tilde (~) tells Vite to look in the node_modules directory for the package.
Also, make sure that you are including the app.css file in your HTML file.
If that doesn't work, try importing the CSS file in your app.js file instead:
import 'tom-select/dist/css/tom-select.default.css';
import TomSelect from 'tom-select';
window.TomSelect = TomSelect;
Then remove the CSS import statement from your app.css file.
Hopefully one of these solutions works for you!