Use monitor location, bank logic, exhaust integrity, and upstream-vs-downstream evidence to separate P2096-P2099 from a bad rear oxygen sensor or a truly weak catalyst.
P2096 through P2099 do not accuse the front of the engine first. They live in the post-catalyst branch, which means the ECU is judging what it sees after the converter. That immediately makes rear oxygen-sensor credibility, exhaust integrity near the converter, and catalyst oxygen-storage behavior more important than they would be for an upstream lean or rich code like P0171 or P0172.
Drivers and even some shops see the words too lean or too rich and jump straight to fuel delivery, injectors, or a front oxygen sensor. That is exactly how money gets wasted. A P2096 or P2099 story can absolutely be rooted upstream, but it can also be created by a rear sensor that is biased, a leak near the rear sensor, or a catalyst that no longer smooths the exhaust stream the way the monitor expects.
If the downstream signal is flat, biased, slow to react, or inconsistent with the rest of the bank, the rear sensor deserves real suspicion. Sensor-wiring damage after exhaust work, heater history, or connector contamination can all make the post-catalyst trim story unreliable. In that situation, replacing the converter first is just buying the most expensive witness before confirming whether the witness was lying.
A true catalyst problem becomes more believable when the engine is otherwise running clean, the exhaust is sealed, the rear sensor is credible, and the post-catalyst behavior stays abnormal through repeated warm drive cycles. Misfire history, sulfur smell, or a previous rich-running event also matter because they explain how the catalyst may have been damaged before the P209x code finally arrived.
A small leak near the converter outlet or rear sensor can add outside oxygen to the sample and make the downstream sensor tell a lean story that the engine never actually created. Bank-specific leaks are especially nasty because they mimic exactly the kind of one-bank problem these codes describe. If the fault appeared after exhaust work or with a new tick, prove the pipe is sealed before you trust the code wording.
On V engines, compare the suspect bank against the healthy bank. If Bank 1 sets P2096 while Bank 2 looks calm, that bank split matters. Also compare rear behavior against upstream fuel trim and O2 activity. If the front of the bank is not telling a lean or rich story, but the rear is, the diagnosis should stay focused on the rear sensor, exhaust path, and catalyst instead of wandering randomly into the fuel system.
First, review freeze-frame and companion codes. Second, inspect the exhaust path and rear-sensor wiring on the affected bank. Third, compare upstream and downstream behavior on both banks if possible. Fourth, correct active misfire or trim issues that could be stressing the catalyst. Fifth, only after those steps should you decide whether the converter is truly weak or the rear sensor was simply reporting a bad sample.