[SG-35280] Wildcard V2: Apply <Input /> Codemod on `client/branded`, `client/search-ui`, `client/shared` and `client/vscode`

Created by: gitstart-sourcegraph

Problem statement

Migration is required to update our code to use the <Input /> Wildcard component. See parent issue for more context.

Success criteria

All occurrences of the <input /> element are replaced with the <Input /> Wildcard component.

Implementation details

• Rename the Input component variant prop to size.
• Use the Input codemod created here to speed up the migration.

Refs

Sourcegraph Issue Gitstart Ticket

Test Plan

• All <input/> elements are migrated to <Input/> wildcard component.
• No UI diff available

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.