You will see that the ScoreCard table winds up containing an extra field, "rowid" that I didn't specify in CREATE TABLE ScoreCard.
That is SQLite specific, documented under https://sqlite.org/lang_createtable.html#rowid
Except for WITHOUT ROWID tables, all rows within SQLite tables have a 64-bit signed integer key that uniquely identifies the row within its table. …
BTW SQLite's last_insert_rowid() documentation
explicitly refers to "the database connection which invoked the function", so should work with multiple parallel insertions.