Clean up global header spacing (#269398)

## Summary

Fixes size and spacing across header buttons. 

- Sets buttons to 32x32; same as left nav
- Sets gap to 4; same as left nav
- TODO: bring this change to EUI, later

**Before**
Varying gap and buttons sizes
<img width="360" alt="CleanShot 2026-05-14 at 16 05 58@2x"
src="https://github.com/user-attachments/assets/08403278-39a3-479b-be3b-ba2340b8454f"
/>

**After**
All same gap; same size
<img width="320" alt="CleanShot 2026-05-14 at 15 53 45"
src="https://github.com/user-attachments/assets/bdd116e5-7fa6-4c67-bc58-f2deb1673f17"
/>



### Checklist

Check the PR satisfies following conditions. 

Reviewers should verify this PR satisfies this list as well.

- [ ] Any text added follows [EUI's writing
guidelines](https://elastic.github.io/eui/#/guidelines/writing), uses
sentence case text and includes [i18n
support](https://github.com/elastic/kibana/blob/main/src/platform/packages/shared/kbn-i18n/README.md)
- [ ]
[Documentation](https://www.elastic.co/guide/en/kibana/master/development-documentation.html)
was added for features that require explanation or tutorials
- [ ] [Unit or functional
tests](https://www.elastic.co/guide/en/kibana/master/development-tests.html)
were updated or added to match the most common scenarios
- [ ] If a plugin configuration key changed, check if it needs to be
allowlisted in the cloud and added to the [docker
list](https://github.com/elastic/kibana/blob/main/src/dev/build/tasks/os_packages/docker_generator/resources/base/bin/kibana-docker)
- [ ] This was checked for breaking HTTP API changes, and any breaking
changes have been approved by the breaking-change committee. The
`release_note:breaking` label should be applied in these situations.
- [ ] [Flaky Test
Runner](https://ci-stats.kibana.dev/trigger_flaky_test_runner/1) was
used on any tests changed
- [ ] The PR description includes the appropriate Release Notes section,
and the correct `release_note:*` label is applied per the
[guidelines](https://www.elastic.co/guide/en/kibana/master/contributing.html#kibana-release-notes-process)
- [ ] Review the [backport
guidelines](https://docs.google.com/document/d/1VyN5k91e5OVumlc0Gb9RPa3h1ewuPE705nRtioPiTvY/edit?usp=sharing)
and apply applicable `backport:*` labels.

### Identify risks

Does this PR introduce any risks? For example, consider risks like hard
to test bugs, performance regression, potential of data loss.

Describe the risk, its severity, and mitigation for each identified
risk. Invite stakeholders and evaluate how to proceed before merging.

- [ ] [See some risk
examples](https://github.com/elastic/kibana/blob/main/RISK_MATRIX.mdx)
- [ ] ...

Author: ryankeairns

src/core/packages/chrome/browser-components/src/project/header.tsx

@@ -39,6 +39,7 @@ const getHeaderCss = ({ size, colors }: EuiThemeComputed) => ({
     // needed to enable breadcrumbs truncation
     min-width: 0;
     flex-shrink: 1;
+    gap: ${size.xs};
   `,
   breadcrumbsSectionItem: css`
     min-width: 0; // needed to enable breadcrumbs truncation
@@ -106,6 +107,13 @@ export const ProjectHeader = React.memo(() => {
     background-color: ${euiTheme.colors.backgroundTransparent};
     border-bottom-color: ${euiTheme.colors.backgroundTransparent};
     padding-inline: 4px 8px;
+
+    .euiHeaderSectionItemButton {
+      block-size: ${euiTheme.size.xl};
+      inline-size: ${euiTheme.size.xl};
+      min-inline-size: ${euiTheme.size.xl};
+      padding-inline: 0;
+    }
   `;
 
   return (
@@ -133,7 +141,12 @@ export const ProjectHeader = React.memo(() => {
               </EuiHeaderSectionItem>
             </EuiHeaderSection>
 
-            <EuiHeaderSection side="right">
+            <EuiHeaderSection
+              side="right"
+              css={css`
+                gap: ${euiTheme.size.xs};
+              `}
+            >
               <EuiHeaderSectionItem>
                 <HeaderNavControls position="center" />
               </EuiHeaderSectionItem>
@@ -142,13 +155,7 @@ export const ProjectHeader = React.memo(() => {
                 <HeaderHelpMenu />
               </EuiHeaderSectionItem>
 
-              <EuiHeaderSectionItem
-                css={css`
-                  gap: ${euiTheme.size.s};
-                `}
-              >
-                <HeaderNavControls position="right" />
-              </EuiHeaderSectionItem>
+              <HeaderNavControls position="right" />
             </EuiHeaderSection>
           </EuiHeader>
         </div>