Update typescript configs for better in-editor support

[rak-phillip]

Summary

This enhances in-editor typescript support by

• ensuring that shell/types/vue-shim.d.ts is included in the typescript config
• removing vue2 type augments from shell/types/vue-shim.d.ts
• updating typescript to 5.6.3

Fixes #12893

Technical notes summary

I tested this change in Zed, Webstorm, and VS Code - typescript support appears to be improved across the board with regards to properly detecting aliased imports and detecting Vue augments.

VS Code allows for selecting the typescript version; developers can choose to use VS Code's version or the workspace version. Later versions of Typescript appear to better handle multiple tsconfigs, so updating typescript to 5.6.3 resolves the import issue nicely. This is also the default version that is currently used in VS Code as of writing.

NOTE: Make sure to run the Vue: restart Vue and TS servers VS Code action after checking out this change

Areas or cases that should be tested

In-editor typescript support. We want to ensure that aliased imports of components work across the board. We also want to ensure that this.$t() and this.$store() are properly detected in component scripts.

Areas which could experience regressions

This should enhance in-editor typescript support, but keep an eye out for new invalid typescript warnings that might not have been present before.

Screenshot/Video

Component imports no longer display errors

Store getters no longer display errors

Checklist

• The PR is linked to an issue and the linked issue has a Milestone, or no issue is needed
• The PR has a Milestone
• The PR template has been filled out
• The PR has been self reviewed
• The PR has a reviewer assigned
• The PR has automated tests or clear instructions for manual tests and the linked issue has appropriate QA labels, or tests are not needed
• The PR has reviewed with UX and tested in light and dark mode, or there are no UX changes

[mantis-toboggan-md]

LGTM - I've looked through typescript vue components and .ts files, I didn't see new invalid errors introduced, and old invalid errors about $store and $t have been resolved.