Is using the siwak immediately before prayer, swallowing the saliva afterward, and without rinsing the mouth, a correct practice, and did the Messenger of Allah, may Allah bless him and grant him peace, do so?

Using the siwak before prayer is a Sunnah of the Prophet, peace be upon him, as he said: "Were it not that I would overburden my Ummah (or the people), I would have commanded them to use the siwak with every prayer." Rinsing the mouth after using the siwak is not obligatory. If blood comes out, he should spit it out and rinse his mouth. If food particles come out, it is better to remove them with a tissue, but if he swallows them, there is no sin upon him. Prohibiting the siwak before prayer or making rinsing obligatory after it is an innovation (bid'ah). The wisdom behind using the siwak at the time of prayer is the cleanliness of the mouth and the honor of worship, and for a matter related to the angel who listens to the Qur'an from the worshipper.