This is what I shared before. But few sajha friends told me 'hawa'. As per my attorney, if you file TPS when you have pending asylum, you pending asylum will go on hold. And any interview dates if you have already scheduled will also be cancelled and it will be rescheduled again.
As per the attorney, you cannot have two immigration benefits at the same time, TPS and Asylum are both immigration benefits to a non-resident aliens.

Do not know how long it takes to get the interview rescheduled, but my attorney stated that you will come to the long queue, and maybe your interview date will be also pending.

Note: All the above information is from an experienced Immigration Attorney. I am just passing it here. I also have a pending asylum and I was strictly told not to file TPS if I want my asylum case to have the interview. My interview was already scheduled when this TPS came into picture.