## What kind of change does this PR introduce?
UI polish for split buttons (primary action + dropdown chevron).
Follow-up to #49055.
## What is the current behavior?
The focus ring sits above the neighbouring half, but the inner edge
stays square, so the ring has two sharp corners at the join.
## What is the new behavior?
On keyboard focus, the squared-off edge uses a slight radius so the ring
matches the outer corners more closely. Resting state is unchanged.
Split-button callsites now share the same join classes as the
design-system example.
| Before | After |
| --- | --- |
| <img width="1030" height="296" alt="43471"
src="https://github.com/user-attachments/assets/9df3bd72-c7ac-4419-ae18-a7e649dc2d66"
/> | <img width="1056" height="276" alt="CleanShot 2026-08-17 at 10 45
09@2x"
src="https://github.com/user-attachments/assets/52e8a4dc-9c52-45ce-b4d0-f0e7b1b75935"
/> |
## To test
Tab to each half (labelled button, then chevron). Inner corners of the
focus ring should be slightly rounded, not square.
1. [Split with
dropdown](https://design-system-git-fix-split-button-focus-radius-supabase.vercel.app/design-system/docs/components/button#split-with-dropdown)
(no login)
2. [Access
Tokens](https://studio-staging-git-fix-split-button-focus-radius-supabase.vercel.app/dashboard/account/tokens)
→ Generate new token
3. Any project on [studio
staging](https://studio-staging-git-fix-split-button-focus-radius-supabase.vercel.app/dashboard/_/settings/general)
→ Settings → General → Restart project
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
- **Accessibility**
- Added accessible labels to dropdown and export controls.
- Improved keyboard-focus visibility, layering, and rounded edge
treatment across joined buttons and menus.
- Removed misleading or redundant screen-reader text and titles.
- **Bug Fixes**
- Prevented split-button controls from shrinking or displaying awkward
borders and corners.
- Refined hover and focus behavior for action buttons throughout
settings, database, storage, account, and documentation interfaces.
- **Documentation**
- Clarified guidance for using overflow menus and responsive
split-button actions.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
## Summary
- Add `button-split-dropdown` and `admonition-button-split`
design-system examples for primary action + chevron menu.
- Document the shared middle border pattern (`-ml-px`, `hover:z-10`;
avoid `border-l-0`) in Button and Admonition docs.
- Mirrors the approach established in the custom SMTP email templates
admonition.
## Test plan
- [ ] Open design-system site and verify `Button → Split with dropdown`
preview renders correctly
- [ ] Open `Admonition → Split button with dropdown` preview and confirm
middle border looks correct on hover/focus
- [ ] Confirm peek code shows the documented class names
<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit
* **New Features**
* Added new split-button dropdown live demos, including
icon/chevron-triggered menus with actionable items.
* Added an admonition demo demonstrating a split primary button plus
dropdown trigger with responsive layout.
* **Documentation**
* Expanded “Split with dropdown” guidance with pairing/when-to-use
rules, required styling/border behavior, and responsive layout
instructions for the primary + chevron actions.
* Updated button documentation heading capitalization to match
typography standards.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
Danny White