The asylum procedure will certainly become a lot slower if Trump does not get re-elected even if there was no pandemic because:
1) The USCIS hired too many extra asylum officers in the past 3 years, which is part of the reason for their financial crisis. Just compare the number of interviews conducted in 2016 vs 2019 and you'll see the huge difference. They were planning on hiring more AOs before the pandemic but it won't happen. The administration's policy of using under-trained AOs is heavily criticized and we will see a reduction in the number of AOs that do affirmative interviews. They will probably relocate some of their forces to the border to do credible fear interviews.
2) The southern border will be re-opened and the immigration court waiting time will increase drastically as a result of migrants flowing in.
Add the effect of pandemic-induced slowdown to the above and you face a wait time of 5-6 years to get an interview if you're lucky. Don't forget that if you applied during the pandemic, you will be definitely buried underneath a heavy backlog because more people apply after you while the asylum office does no interview and the LIFO system will screw you later. The asylum offices don't do shit right now. My lawyer had only one interview at the Chicago office within 2 months after they reopened.
Finally, Biden called the COVID-related travel ban that Trump imposed on China Xenophobic. China is the second largest source of affirmative asylum applicants in the US and I could imagine Biden ending the travel ban just to look like a good old Democrat. Once the US embassies start issuing tourist visas again, the asylum scene will turn into a real shit show.