Very interested in the answers. I would guess that most big websites use stored procedures.
I use Dapper in C# to access stored procedures and it's blazing fast. Unfortunately, most medium to large companies tend to use Entity Framework, which is a bloated beast of an ORM which sadly creates a void between a company's development team and database administrators, especially if the company decides to develop their database in Entity Framework using "code first" methodologies
When we were building a big app 10 years back, we used ORM for user facing modules and stored procedure for batch processing such as CSV import/export. We would clear the ORM cache for every SP run which are usually scheduled at mid-night to avoid stale data.
These days, it is graph DB (such as firebase) for user facing module. It syncs data into a warehouse (such as BigQuery) that we use for batch processing.