Transmission issue

You could change them, but check fuel pressure with a gauge and clean throttle body on both sides and IAC hole with choke cleaner that may be part as well. See link.
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator
https://www.2carpros.com/articles/throttle-actuator-service

Which model Pontiac? When was the last time the transmission was serviced? The bog in reverse and slow engagement in drive both indicate sealing issues inside the transmission. Does it get worse or better once the engine is up to operating temperature? If you step down LIGHTLY on the gas and raise the rpms, does it still bog?

Yeah that sounds typical of worn and stiff seals on the various parts in the transmission. When new they are soft and flexible but they get hard with age and heat. When they get cold they shrink a bit, not an issue when they are still flexible but once they age they don't seal well when cold. Once the trans fluid gets warm they soften some and seal better. You could try adding some Lucas trans additive, it sometimes works, but I wouldn't expect a miracle.

The real repair would be to tear the trans down and replace the worn and old parts. That is a tough call unless the rest of the car is in real good shape.