Fixing ts-build errors and build config from webpack-to-vite merge

[seunomonije]

Fixes an issue found in #7687 where artifacts were not properly building with Vite. The appropriate CI output can be found here. See discussion in original PR for more details.

The issue stems from the fact that Vite does not allow handling multiple entry points from an array in configs, which is different than Webpack. A common alternative is to use separate config files for each entry point, but this PR leverages Vite's --mode flag to allow bundling from one file. Should the number of widgets in cirq-web grow, it may be worth looking at consolidating the widgets in one entry point, but that seems like overkill for now.

The large line count is due to how Vite bundles the TS, but the file size is still comparable to the old bundle files (501KB versus 503KB).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.38%. Comparing base (e8e79bb) to head (81c946f).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@ Coverage Diff @@ ## main #7697 +/- ## ======================================= Coverage 99.38% 99.38% ======================================= Files 1089 1089 Lines 97550 97550 ======================================= Hits 96949 96949 Misses 601 601 

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[pavoljuhas]

Thank you for the fix!