The character record for the Kensai indicates the "Number of Attacks" at 3/2. It doesn't change despite character advancement or increased proficiency. I have no idea if this is just a typo or the Kensai is not getting any more attacks. Both the Level Up and weapon proficiency descriptions indicate an increase in the number of attacks but this is never reflected on the character record.
I can switch to a non-proficient weapon and the "Number of Attacks" changes to 1.
The following "Number of Attacks" are somewhat confusing to me, although they may be correct. Neera has 3 attacks for Darts while Xan has only one attack with the Sling. Imoen gets one attack with the Whistling Sword (+2 short sword, speed 1) but 2 attacks with a +1 Short bow (speed 5). All characters have one proficiency point with the appropriate weapon.