No, you cannot visit Qatar for tourism purposes with a transit e-visa. A transit e-visa is specifically designed for travelers who have a layover in Qatar and wish to leave the airport to explore the country during their transit. It allows you to spend a short time in Qatar while en route to your final destination but is not intended for leisure or tourism purposes.
If your primary purpose is tourism, you should apply for a Qatar tourist visa or the appropriate tourist visa category, which is specifically designed for tourists wanting to explore and enjoy the country's attractions. Always ensure that you have the right visa for your intended activities to avoid any legal or immigration issues during your visit to Qatar.