Hi Katie,
I was STD for 6 months through work that transitioned to Long Term. My LTD company also required SS disability. I applied directly with social security. My reduced salary is basically split between the two entities with SSD paying a little more than half per month than the LTD. Once they find out that I was not fraud, it took about six weeks. The SSD website states that the average wait time is 200+ days. Also, you are paid once per month at the end of the pay month.
It’s a process.
Good luck with your pancreatic cancer. I had 9 FOLFIRINOX then the Whipple then three more FOLFIRINOX. I just had my six month scan and it was clean.

Best,
Steve