I faced the same trouble with the permission issue when trying to setup on Synology (Linux). Came. up with below script and now works perfectly. If its helpful for someone, here it is:

#!/bin/bash

appDir="/opt/data/youtrack/youtrack_data"

sudo mkdir -p -m750 "${appDir}"/{data,conf,logs,backups}
sudo chown -R 13001:13001 "${appDir}"

sudo docker run -d --restart unless-stopped --name youtrack1 \
-v ${appDir}/data:/opt/youtrack/data \
-v ${appDir}/conf:/opt/youtrack/conf \
-v ${appDir}/logs:/opt/youtrack/logs \
-v ${appDir}/backups:/opt/youtrack/backups \
-p 8146:8080 \
jetbrains/youtrack:2025.1.64291

Reference:

• https://www.jetbrains.com/help/youtrack/server/youtrack-docker-installation.html#create-and-configure-directories