You are correct in your assessment. In a shared view, Airtable doesn’t give you the ability to expand the linked records to see more details about those linked records.
A very clunky workaround is that you could also share a view from the OTHER TABLE, and distribute that shared link as well.
You could even create a formula that creates a URL for each record in your OTHER TABLE, and then lookup that URL into your original table. So when people are looking at your original table, they can click on one of the URLs to open up that linked record in the other tables’s shared view.
For an easier way of handling all of this, you could pay for MiniExtensions.com, which lets you create shared views that let you expand linked records, and you can choose which fields you’d like to show for those linked records.