Is the repentance of one who claimed to apostatize from Islam to facilitate their asylum accepted, and do they remain Muslim?

What you have done is a grave sin and a serious transgression. Speaking a word of disbelief (kufr) or doing that which necessitates disbelief is impermissible for the sake of achieving any objective, except in a state of duress, and it signals the complete loss of religion, unless its perpetrator repents with a sincere and heartfelt repentance. Ibn al-Qayyim said: "There is no disagreement among the Ummah that it is impermissible to allow speaking a word of disbelief for any purpose, except for one who is coerced, provided his heart is firm in faith." You have no escape from this affliction except to repent to Allah, majestic is His glory, and return to your Islam anew, and renew your faith by uttering the two testimonies of faith (Shahadatayn), and establish the matters of your religion, and keep yourself away from places of temptation with shirk (associating partners with Allah) and its people. Allah Almighty says: (Except for those who repent, believe and do righteous deeds. For them Allah will change their evil deeds into good ones. And Allah is Oft-Forgiving, Most Merciful).