In Steam\userdata\[userid]\config\grid

Every game with a custom logo position has a .json file by the game of [gameid].json

A typical .json file will look like this:

{"nVersion":1,"logoPosition":{"pinnedPosition":"CenterCenter","nWidthPct":66,"nHeightPct":92}}

So, now I can batch process all logos to be in the Center by creating files and using this .json

Refresh the library to see the changes.

This info is also stored at:

Steam\userdata\71362629\config\librarycache

albeit in a slightly different format.

Changes may get reverted if editing these files in librarycache, editing the .json files in \grid folder turns out to be simpler (since Steam will fix any weird things that pop up, but keep your custom position changes)