Minor issues with DDG's styling.

### Is there an existing issue outlining your problem?

- [x] I have searched the existing issues and they do not solve my problem.

### What userstyle are you seeing the problem on?

lbl:duckduckgo

### Description

The typing field in search is a solid square that peeks outside of the pink-ish outline on the left hand side, and the search button is unthemed/gray instead of the catppuccin style.

The entirety of the entirety of https://duckduckgo.com/ is unthemed.

### Relevant screenshots

### Browser version(s) this issue occurs on

Zen 1.20b [Build ID: 20260524090131]

### Stylus extension version

Stylus 2.3.24

### Installed version of the userstyle

2026.03.18

### Any additional comments?

_No response_

Start by opening the lbl:duckduckgo userstyle and reproducing the report at duckduckgo.com in Stylus, using the screenshots as visual reference. Trace the search field and search button styling, then check the rest of the page for the reported unthemed areas; done means the field stays within its outline and the controls and page use the Catppuccin style.

Written by the indexing model from the issue text.