Several issues in the shared docs Select component (used by the API reference package filter):

• The options list never scrolled: its element used a class with no styles, so the intended max-height/overflow rule was dead. Point it at the styled class so long lists scroll within the popover.
• Selecting an option now closes the popup instead of leaving it open.
• Clip the trigger and popover corners (overflow: hidden) so their rounded borders render cleanly, and align the popover width with the trigger.
• Drop the selected-option checkmark. The component is single-select and already marks the selection with a highlight, so the tick was misleading.
• Remove the unused disabled input.

PR Checklist

Please check if your PR fulfills the following requirements:

• The commit message follows our guidelines: https://github.com/angular/angular/blob/main/contributing-docs/commit-message-guidelines.md
• Tests for the changes have been added (for bug fixes / features)
• Docs have been added / updated (for bug fixes / features)

PR Type

What kind of change does this PR introduce?

• Bugfix
• Feature
• Code style update (formatting, local variables)
• Refactoring (no functional changes, no api changes)
• Build related changes
• CI related changes
• Documentation content changes
• angular.dev application / infrastructure changes
• Other... Please describe:

What is the current behavior?

The package filter dropdown on the API reference page (the shared docs-select
component) has several issues: the options list doesn't scroll on short pages,
the popup stays open after picking an option, the trigger/popover corners and
widths don't line up, and a checkmark on the selected option makes the
single-select look like a multi-select.

What is the new behavior?

• Long option lists scroll inside the popover.
• Choosing an option closes the dropdown.
• Trigger and popover corners are clipped and their widths match.
• The misleading selected-option checkmark is removed (selection is shown by
  the highlight); the unused disabled input is dropped.

Does this PR introduce a breaking change?

• Yes
• No