>What about Soyuz? IIRC, they haven't lost a manned mission since 1971.

Neither has SpaceX :)

Soyuz is somewhat more complicated since it's an entire family of rockets:

The Soyuz-FG (2001-today, currently does all manned flights) has a 63/63 success record.

The Soyuz-U2 (1982-1995) also has a 72/72 success record.

The Soyuz-U (1973-2017, also manned flight) has a 765/786 (97%) success rate, with no failure in their manned flights.

The Soyuz-2 (2004-today) has a 68/75 (91%) success rate.