Does a Muslim become an apostate due to continuous intrusive thoughts (waswasah) of insulting God, even while maintaining prayer, belief in God, and seeking refuge from Satan when such thoughts occur?

These whispers that contradict Tawhid (monotheism) do not harm the believer in any way, as long as he dislikes them and recoils from them. In fact, his dislike of them is a sign of the sincerity of his faith and the soundness of his conviction.

The believer is afflicted with the whispers of Satan and the whispers of disbelief, which constrict his chest. Disliking these whispers and repelling them from the heart is a sign of pure faith. Similarly, considering it a grave matter to speak of them and fearing them intensely is pure faith.

Satan whispers to those he despairs of leading astray. As for the disbeliever, he comes to him from any direction he pleases.

Whoever experiences this should seek refuge in Allah, cease entertaining those whispers, turn away from these false thoughts, and resort to Allah Almighty to remove them.