Is it permissible to kill mice in the house using glue traps that cause them prolonged suffering?

The Messenger of Allah, peace and blessings be upon him, commanded us to treat animals with kindness, even when killing them. He said: "Indeed, Allah has prescribed excellence in all things. So, if you kill, then kill well, and if you slaughter, then slaughter well. And let each one of you sharpen his blade and relieve his animal." Therefore, whoever sets a mouse trap (sticky trap) must monitor it, and if they find a mouse stuck, they should kill it immediately out of kindness to it, and not leave it to die of hunger or thirst. If they are delayed in monitoring it due to an excuse like sleep or work, there is no blame upon them. Sheikh Ibn Uthaymeen mentioned that leaving a mouse on a sticky trap to die of hunger and thirst is not permissible, and he used as evidence the hadith of the woman who entered the Hellfire because of a cat she imprisoned.