Are Shadow Assassins proficient with Sawtooth Sabre?

Question

Are Shadow Assassins proficient with Sawtooth Sabre?

In RAW, how proficient is the shadow assassin with the sawtooth sabre?

Weapon and Armor Proficiency
A shadow assassin is proficient in all simple weapons, all light weapons, as well as bolas, net, repeating crossbow (light only), shuriken, spiked chain, and whip. The shadow assassin is proficient with light armor and small shields, but not heavy shields or tower shields.

Sabre, Sawtoothed Category: [light] Proficiency: [exotic]
A sawtooth sabre may be used as a Martial Weapon (in which case it functions identically to a longsword).
If you have the Exotic Weapon Proficiency (sawtooth sabre) feat, for the purpose of two-weapon fighting you can treat it as a light melee weapon; for all other purposes, it is a one-handed melee weapon.

Here's scenarios we've been discussing:

1. SA can not wield SS proficiently, since the SS is an [exotic] weapon.
2. SA can wield SS proficiently, but cannot use it as a [light] weapon due to lacking the Exotic Weapon Proficiency feat.
3. SA can wield SS proficiently and as a light weapon, since the SS is a [light] weapon and SA have proficiency in "all light weapons".

Answer 1

Shadow Assassins are not Proficient in any way

The source you used is outdated; Archives of Nethys has the actual current version of sawooth sabre that is Category: One-Handed (as it should be based on how it's written).

It is not a Light weapon as of its most recent printing, and Shadow Assassin does not have Longsword proficiency, so they are unable to wield the weapon proficiently at all.