Is a person's fear and remorse after committing major shirk considered repentance? And is the subsequent tranquility of their heart a sign that their repentance has been accepted? If not, what is the solution?

A person's weeping over what they have fallen short in and their sorrow for it is remorse, through which the acceptance of their repentance is hoped for. Therefore, they should praise Allah, have a good opinion of Him, and be reassured by the vastness of His bounty and forgiveness. Let them do what is best for their heart and most helpful in obeying their Lord, and let them frequently seek Allah's forgiveness and ask Him to accept their repentance.