So got my 2nd toolkit today and didn't get a sparrow. My understanding is that item is a 100% at 1 of 5 sparrows.
https://www.bungie.net/en/Vendors/Item?category=0&item=797951392&vendor=3917130357
If you want to check.
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Same thing happened to me. Got all of the sparrows except for the EV-43 Lightrunner and expected to get it after handing in my S license quest and opening the Toolkit reward. It didn't give me anything, and when I hover over the Lightrunner in the kiosk it says "Requires Eververse License" but when I go to the Eververse store and hover over the kit it says all items owned. And no, my sparrow slots weren't all full.