Is there a GPS super tiny for passerine birds?
The technology is not there (yet) for deployments on 10 gram birds. The limits for GPS technology are around the 50 g range, for birds. Also bear in mind that the smallest loggers are generally not capable of transmitting, so you would need to recapture the animals to retrieve your data.

As your question implies, there is a strong trade-off between device weight and battery life. There are GPS devices weighing as little as 1 g, but their lifespan is very limited (10 fixes for the 1 g device; 50 for a 1.1 g device).

As a side note: your question implies that small passerines can carry 20 - 50 % of their body mass in tracker without their flight being affected. The ethics boards I am familiar with generally limit trackers to ~ 5 % of the mass of the animal.