02 cadillac seville sts - slow to engage reverse and first gear

I bought this Cadillac down at auction. It was giving me misfire codes. I replaced both banks of volt packs and all 8 spark plugs and I'm not getting any kind of misfire code anymore and it's making up the hill and running good. The only issue I have left is the fact that when I go into reverse or just starting in first I really have to push pedal down for it in catch. Like it was slow to accelerate or go in reverse. Does anybody have any idea what it could be? found a bunch of similar issues on Google but no one had any solutions

Do you mean the trans fails to engage or the engine is unresponsive?

I would imagine it's something with the transmission, because when I step on the gas pedal I can hear the engine revving up then it finally seems to catch.

The low/reverse band may be slipping. This could be due to the band itself, the band pin or anchor, or the actuator/accumulator. Fortunately, the servo, its link pin and the accumulator can be serviced through the lower pan (in the lower valve body). It is not anywhere near as expensive as transmission removal. Any reputable transmission shop will be able to diagnose this.