I cannot reproduce this problem. I just reverted all assets to the initial state that your repro-package came with, still this issue does not occur. I only see the incorrect light/dark changes on the trees (with SpriteRenderer components), but not on the medikit, also not on the character.
Can you show a screenshot or video of the medikit when it's in dark vs light state?
You are right, it turns out the medkit does not change brightness in the example project I sent. However, I tried duplicating the medkit, and when there are two medkits in the scene, their brightness does change based on the positioning of the player. Similarly, in my full project this brightness change occurs in all pick-up objects except for one. I don't know why.
The following screenshots show the water bottle on the right of the screen becoming brighter when the player shares a similar Z transform value:
They receive proper light. I listed the necessary steps for the Spine/Sprite/Pixel Lit
shader above, it seems as if you did not provide normals as described - then they will be pitch black.
Ah okay, I thought the steps you provided were simply for receiving shadows, which I did not need. I enabled 'Fixed Normals' at the material and now the Spine/Sprite/Vertex Lit objects are receiving directional lighting. It seems this material works for the purposes I need, and the brightness issue doesn't occur. Hopefully using this instead of Spine/Skeleton Lit won't result in any surprises down the line.
I'm curious to know what's going on with that brightness bug, though, if you figure it out. I'm surprised this isn't a common problem that occurs with other users. It makes me wonder what they are doing differently that they haven't come across this behavior, as I feel like I'm just doing some pretty standard stuff here.