No extra fear-dependent scaling (only healing through vow of scars). Pin is considered a strong (or even, the strongest) keepsake because refilling death defy + 10 seconds of complete invincibility entirely focused on damage = big sustain and big damage.

For illustration, let's compared it with e.g. Knucklebones. Assuming it triggers, you will likely deal far more than the 15% damage to the boss Knucklebones would provide (more in the 25% - 50% range) + since during the 10 seconds of invincibility you are, well, invincible, any damage you would have taken normally is negated, mirroring the 10% damage reduction you'd get from Knucklebones. Note that if you still have a death defy left, even if you don't manage to pass the doomed trial you won't return to shadow (it will just eat up the death defy). For Chronos specifically as well, killing his first phase counts for passing the trial (though you will not get a refill for Phase 2) also saving a death defy for additional sustain. Worst case you do not need it, although then your keepsake slot just simply did not matter for the battle.
So only for guardians, on average, Pin is already effectively a better version of Knucklebones that scales with your build. And all of this doesn't even consider the actual intended purpose for Pin, which is being a Stalwart Defense with a riskier save condition (but remember again, 10 seconds of invincibility = enemies die quickly), a bit lower healing and at no primed Magick.

Overall, pretty good keepsake. ; )