Use `const` and `let` instead of `var` in `list_picker.js`

Substituting the last `var` uses in forms/resources. The rest of the
tasks mentioned in the bug have already been addressed in prior CLs.

Fixed: 41469256
Change-Id: I2d8f109df66be3941ae2d4092e0fcac6fc2de7b4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6663920
Reviewed-by: Mason Freed <masonf@chromium.org>
Commit-Queue: Ana Sollano Kim <ansollan@microsoft.com>
Cr-Commit-Position: refs/heads/main@{#1477677}