Is it permissible to quit working with one's paternal uncle, despite the ease of starting work with him after performing Istikhara, if he treats one badly, coupled with the fear of not finding another job and psychological distress?

It is advisable to be patient with the current job and continue discreetly searching for another one. When found, politely apologize to your uncle with wisdom and transition to the new job after performing Istikhara (prayer for guidance) and seeking consultation. Care must be taken to honor your uncle, be gentle with him, repel his ill-treatment with kindness, and seek Allah's help and piety, which eases affairs and relieves distress.