Search Block: Background wrapper for 'Button Inside' option

[Rishit30G]

Description

This issue is a follow up of #69318

Currently, the ‘Button Inside’ option in the Search Block is missing a background wrapper with a common color as of the input, making the input and button appear separate instead of part of a single container.

Step-by-step reproduction instructions

1. Add a new post
2. Add a new search block
3. From the BlockToolbar option select the 'Change Button Position'
4. Select the 'Button inside' option from the dropdown
5. Notice that only a border around the button and the input appear

Screenshots, screen recording, code snippet

Notice that the even though the border surrounds the button and the input, but as per the 'Button Inside', there is absence of a background wrapper which should cover the button and the input together with a background color as that of the input.

Environment info

• Gutenberg 20.4.0-rc
• WordPress 6.7.2

Please confirm that you have searched existing issues in the repo.

• Yes

Please confirm that you have tested with all plugins deactivated except Gutenberg.

• Yes

Please confirm which theme type you used for testing.

• Block
• Classic
• Hybrid (e.g. classic with theme.json)
• Not sure

[Rishit30G]

This is the redesigned version, which I believe is much more appropriate:

Any thoughts on this would be appreciated before I proceed with implementation. 👍🏻