Indexes can only help narrow down to the issues for the project (more generally: matching rows for the query). Once the index narrows down the rows, Postgres still has to count them all, and Postgres isn't particularly fast at that, especially in an active table[0]. That's what the author meant by 'complete index scan of the tasks for the project'.

Of course this isn't really relevant until there are a very large number of rows to count for a given query. Much larger than what is likely for "tasks in a project". I've run into this only with queries that end up counting 10e7/8/9 rows, i.e. more like OLAP workloads

[0] https://wiki.postgresql.org/wiki/Slow_Counting