Search Box Scope of Standard sites in SP Online Tenant

hi TarunHCC​  Setting a Home Site mainly affects the search experience of the Home Site itself, not all other SharePoint sites in the tenant.

So after configuring the Home Site using:

Set-PnPHomeSite -HomeSiteUrl "https://sharepoint.com"

the expected behavior is:

The Home Site search bar will search across the entire tenant (organization-wide search)

A standard SharePoint site (non-home site) will continue to use its normal search scope

So standard sites will still typically search:

The current site

Or the connected Hub scope (if the site is associated to a Hub)

They do not automatically become tenant-wide search sites just because a Home Site was configured.

So your understanding is correct only the Home Site gets the tenant-wide search experience by default.