It appears that the constraint name reported under INFORMATION_SCHEMA.TABLE_CONSTRAINTS.CONSTRAINT_NAME is always ‘PRIMARY’ for every primary key constraint, regardless of what name was specified in the CREATE TABLE DDL. The same goes for the corresponding index reported in INFORMATION_SCHEMA.STATISTICS.INDEX_NAME.
Note that for unique constraints and foreign key constraints this is not the case.
I was also a bit surprised that both for reference and sharded tables every primary key index always appears twice in INFORMATION_SCHEMA.STATISTICS. Once with INDEX_TYPE ‘BTREE’ and once with ‘SHARD’. But this is maybe to be expected.