Is abandoning the 'Isha prayer and sleeping through it due to the fear of obsessive thoughts (waswas) concerning ablution and abandoning prayer considered "intentionally abandoning prayer," thereby necessitating ghusl or leading to apostasy? And in this case, is ghusl required, and must both the 'Isha and Fajr prayers be re-offered?

There is no cure for obsessive thoughts except to ignore them. Sleeping after the prayer time has begun, without taking measures to wake up, is a mistake that necessitates repentance. You did not intentionally miss the prayer, so there is no need to worry. Intentionally missing a prayer is a grave sin, but it is not disbelief (kufr) according to the majority of scholars. Therefore, what applies to an apostate does not apply to you. You are still a Muslim, and you must repent. The time for the 'Isha prayer extends until the appearance of dawn, according to the majority of scholars.