How to delete a SQL Server instance completely and cleanly?

I'm having some trouble understanding the relationship between a SQL Server connection and an installation of SQL Server.

When I started doing sysadmin kinds of things, I installed SQL Server 2025 on my system twice. (This was due to a misunderstanding of how connections work, which led me to think the first installation had failed.) I have since deleted one of the installations through the SSMS Connect dialog. Now the Connect dialog shows only one SQL Server 2025 connection, and Add or Remove Programs shows only one instance of SQL Server 2025 (I suspect that it always did), but the second instance's subfolder is still present in the C:\Program Files\Microsoft SQL Server\ folder.

So the second instance seems to be uninstalled in one respect, but still present in another. What is the state of this instance? Can I simply delete its subfolder to finish the job, or must I do something else to remove it completely and cleanly?