Is it permissible to leave the mosque without performing tasbihat?

Tasbihat can be performed individually or in congregation. Since it is an act of devotion that is independent of the prayer and is recommended to be performed, omitting tasbihat is not considered a deficiency in the prayer itself. Therefore, it cannot be said that it is impermissible to leave the mosque after prayer without performing tasbihat. However, it should not be forgotten that this is a great opportunity to remember Allah and seek His pleasure.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu