Versatile Thermostat: a full feature thermostat (energy, door/window, presence, motion, preset, ... management)

Exactly. With slow latency and long cycle, the algorithm TPI is not totally accurate. There is no error accumulation to regulate in long term. Maybe an implementation of a PID algorithm will be more suitable for thoses case, but the complexity of configuration and tuning of such algorithm discouraged me from continuing until now.

FYI you have a PID algorithm implemented here: Smart Thermostat - le chauffage contrôlé par PID - #188 par ScratMan - Intégration - Home Assistant Communauté Francophone . Maybe it could helps
(in French forum).