Could be the upstream O2 sensor at fault here. At lower throttle positions, it is setting up all the feedback, but at WOT, it will drop into open loop mode (preprogrammed air/fuel map). Toyota tends to be on the conservative side on that tune, so it will run a bit rich at WOT. Since you are running rich, possible the prebuilt map is no longer in range.

Could also point to bad injectors. A number of the ZZ family of engines have seen injector failures, especially with a lot of mileage on the engine. Sometimes it is as simple as a grommet on the injector leaking, Could also be the injector running outside of spec, ie, the ECM is forcing the injectors to run higher than normal duty cycles to feed more gas in than usual, can kill an injector faster.

Nope - at WOT, it should go into open loop - pretty much every car I've seen does that.

Very possible that the O2 sensor is "lazy" - meaning that is still working, but not as optimally as it should. Many times, these sensors will not outright fail, but die slowly - many times, the CEL will not even illuminate.

Possible that the old sensor is still working. I know on this engine family - it is very sensitive to the brand of parts that you put on it. Especially with the O2 sensors, they recommend staying with Denso parts. I've used Walker and Bosch replacements, both caused engine drivability issues - ended up replacing them with Denso O2 sensors, problem solved.

It is always a good idea to reset the ECM and clear those codes - see if the codes come back or new ones pop in their place.

The freeze frame data looks OK to me - mine are pretty similar. Nothing in there screams as a potential problem yet - except for the fuel trims. Short term can fluctuate in sub-seconds scale, but usually tries to stay within a couple tens of percentage. Long term fuel trim shouldn't exceed double digit percentages. Rule of thumb, add STFT and LTFT together, should not exceed 10% total trim, if it is more (positive or negative) - then the ECM has to pull or push an excessive amount of fuel to get the engine to run within spec. The absolute max range between them is also important - like to keep them less than 10% trim variance in total.

As for the weird hesitation, it does sound like a feedback issue to me - the engine cannot react fast enough to changes in input. That points to MAF, O2 sensor, TPS, or even the ECM. Hard to say for certain without being right infront of the car and doing some more diagnostics. If it is electrical - could be a nightmare to diagnose, as they can be very intermittent and/or hard to track down.

Might try capturing data when you keep the RPMs steady at 2500 RPMs, see what the trims do. If the STFT bounces around a lot, that is OK, but the LTFT should stabilize at a fairly low percentage. If it doesn't - really points to a possible MAF issue. If neither one of them changes much (low or high) - that could point to a potential O2 sensor issue. Possible it could be multiple ones issue compounding each other.

Noise could be from the VVT-i - changes the valve overlap on the intake side, so it could cause that induction noise. Vacuum leaks are usually a higher pitched, hissing kind of noise.

LTFT valves at 2500-2600 RPMs look good, at 3K, they look a bit high, but still within reason.

Whining, high pitched noise could be from a noisy bearing from the accessories - like the alternator. little too high pitched to be a vacuum leak, but shouldn't rule out that possibility.

Those other recordings are pretty helpful. I can hear that very pronounced "dead" spot right before the engine revs up. That is really unusual. Almost like the ECM is lagging in its feedback to the rest of the engine. Almost like it is overshooting the amount of fuel needed for that amount of throttle application - only once it figures out what the right mix is, then it stabilizes and the engine revs up like it should.

I'm assuming by the model year that this car still uses the cabled throttle body and not the DBW setup?

Unfortunately, lots of things can cause what you are experiencing. Sensors to electrical - to induction and exhaust issues. Since you are consuming a fair amount of oil - possible plugged catalytic converter is a real possibility. Also would do a number on your O2 sensors, more so if you run a higher mileage oil, as their additive packages, though great for older engines - protection and lubrication wise, can slowly kill these O2 sensors and catalytic converters more quickly.

Possible that the MAF is bad. That stumbling at higher RPMs is just a feature of not having the MAF connected, car runs in limp mode to save the engine. Another possibility, is that with the MAF off, the car is running off of preset air/fuel maps and other feedback sensors (O2 and TPS) - could point to those sensors being offset, causing the MAF to "appear" faulty.

But you could be on to something. That sort of behavior when you disconnect the MAF, usually points to either bad MAF or vacuum leak.

Vacuum leaks can be nightmare to track down. Some only leak dependent on temperature - some only under movement. Spraying something on the hoses and unions is the quickest way to check them. You'd almost have to pull each hose off and inspect it. Check around the induction system and look for cracks in the airbox, especially close to the MAF. Gaskets, might have to pull off the TB and intake manifold if you can't see all the way around.

Unplugging the O2 sensor would have a different effect than the MAF trick. Some cars, makes it completely undriveable - some will fall under a limp home mode. Don't remember what the Toyotas does off the top of my head, their tuning is pretty conservative - might drop into a limp , degraded performance mode.

Just replace - electrical parts like that can be intermittent - this is one of those swap and see sort of part. Even if it diagnoses OK, it could still be faulty. Double check the return policy on the replacement parts, some retailers won't take back electrical parts once they touch the car - just in case the MAF is not the culprit.