Tab Search: UX review audit related changes

UX audit related changes:
- Search field, list item, and feedback footer height changes
- Search field background color and styling changes
- Component alignment related changes

Dependends on CL:
https://chromium-review.googlesource.com/c/chromium/src/+/2417548

Screenshot:
https://drive.google.com/file/d/1ahWvFnnpFgJOJXgWqDihMZFcoE0KLzf3/view?usp=sharing

Bug: 1128599
Change-Id: I231688d955cbda00c4109dd48ddb5eed77f94165
Reviewed-on: https://chrome-internal-review.googlesource.com/c/chrome/browser/resources/tab_search/+/3276513Reviewed-by: John Lee <johntlee@chromium.org>
Reviewed-by: Tom Lukaszewicz <tluk@chromium.org>
Cr-Commit-Position: refs/heads/master@{#819609}

chrome/browser/resources/tab_search_merge/app.html

@@ -23,7 +23,7 @@
   #feedback-footer {
     border: none;
     border-top: 1px solid var(--google-grey-refresh-500);
-    height: 32px;
+    height: 40px;
     width: 100%;
   }
 

chrome/browser/resources/tab_search_merge/tab_search_search_field.html

 <style include="cr-icons">
   :host {
     align-items: center;
-    background-color: var(--google-grey-refresh-100);
-    border-radius: 32px;
+    background-color: var(--mwb-background-color);
     display: flex;
-    height: 28px;
-    margin: 8px;
-    padding: 0 8px;
+    height: var(--mwb-item-height);
+    padding: 0 var(--mwb-list-item-horizontal-margin);
     user-select: none;
   }
 
-  @media (prefers-color-scheme: dark) {
-    :host {
-      background-color: var(--google-grey-800);
-    }
-  }
-
   #searchIcon {
     height: var(--mwb-icon-size);
-    padding-inline-end: 4px;
+    padding-inline-end: var(--mwb-list-item-horizontal-margin);
     width: var(--mwb-icon-size);
   }
 
+  #searchInput {
+    padding: 0;
+  }
+
   @media (prefers-color-scheme: dark) {
     #searchIcon {
       color: var(--google-blue-refresh-300);