2005 Toyota Rav4 P0171 with LTFT at +44

Hello, I am working on the 2005 Rav4 that has issues after 3 years of storage.
The owner started car with 3 year old gas after changing new battery. Needless to say it was running very rough so she took it to nearby Ford service who pulled misfire and P0171 codes and said that the engine is bad and the car is junk.
I've found the following:
uniform compression 175
dead miss on cylinder #1(bad coil , changed, fixed)
weak cylinder #4 , non- ignition misfire, (checked by switching coils) cleared on it's own
black carbon covered spark plugs (replaced)
loose AFR sensor (tightened)
Added 3 gallons of fresh gas
cleared codes and took for the ride
P0171 came back with LTFT +44; not affected by engine speed or load.
The reading of secondary O2s pointing to lean mixture correction (0.3Volts)
Main AFR is switching
spark plugs are clean (slight yellow tint) as well as AFR sensor tip
MAF reads correctly (rpm/500* 2.4L)
Fuel pump is holding pressure (engine idles for 20 to 30 seconds with pump unplugged)
The pulsation damper screw is raising quickly and is firm to touch when engine at idle
I took the pump assembly out, the gas in tank is transparent and not yellow
The regulator is not leaking at 20PSI ; the pump had slight whine which is even less noticeable after installing clean inlet filter sock
The "after pump" filter has been changed some time ago
Any other tests I can do without fuel line pressure gauge?
Thank you in advance!

There is a chance that the flow through the injectors is restricted and you may want to run some cleaner through them.

Where did you come up with that air mass formula ?

Formula is from this site tunertools.com/pages/load-control-and-calculation converted it to metric units (grams per second)
The injectors are definitely were on my to do list (after checking the fuel tank for contamination and fuel quality)
Also, the replacement battery is not much better than the original dead one and will be tested and charged or changed.
Swapping the battery will likely reset LTFT to zero so I will see the initial condition
before correction
This problem was very similar but without pressure tester I was only able to check pump unit for obvious pressure loss (and it's holding)

You - or I - may have misinterpreted the given information to air mass (theoretical mass air flow)....

A popular formula I like to use goes like 1 gram per liter engine displacement at idle and 40 grams per liter at 5000 rpm.

I am aware that this rule is NOT 100% correct but I feel comfortable to use it as a first aid.... (some will say this formula is valid only on engines 3 liters and bigger, others state it's 1.2 grams per liter at idle).

I would agree that you have fuel starvation and that is the direction I would be going.

A quick test you could do is to feed a fuel source (propane) into the air intake and see if the fuel trim comes down. The fact that there is an extra 44% of fuel being added and the o2 sensor is still lean says there is a fuel issue.

Update: used injectors from 06 Scion (tested and cleaned)
solved the issue: after short drive the LTFT became +12.5 and secondary O2 measured .850V (it should go close 0 even more)
I used 7.8 by 1.9mm Viton o-rings black (Shore A70)
I tried to put injectors in with stone hard insulator ("worked" back in 2005 on my 87 Camry) but got major leaks around them (verified by spraying carb cleaner into each cavity)
So I took them out second time and installed new insulators!
While many leaking hose connections will create small vacuum leaks, as long as the car passes smog I can address this latter. The second picture shows my "smart "special tools including fuel pump primer switch (plugs into the fuse box in place of the FP relay (labeled as COR)
Fuel injector actuator
Fuel tank pump cover plug (when pump is out) injector cleaning hose
it is filled first with cleaning solvent than the red tube part is installed and the canned air is sprayed in while pushing the switch to open injector

Good news then.....

You may want to recheck the total trim after a while because +12% still is a bit high and close to setting a code. If the numbers do not go down further you could try to service the injectors in an ultrasonic laboratory..

Thank you for the feedback.

I will see how it will behave on idle vs 2500 rpm and make sure that the downstream O2S stays close to .450 V I f it remain at .850 the AFR is marginal and needs to be replaced (Reading the downstream O2S can save time using exhaust sniffing (smog test) probe).
It was possible to start the engine wit intake removed and MAF disconnected; I also primed the system to check for gas leaks.Cleaning around injector holes in the head was fun stuff; I used mirror and light to see what I was doing

More updates:
LTFT went down to +7 (two known very small vacuum leaks)
Downstream O2 reads 0.760 after warm up
No pending codes or gas smell (I reused fuel pump top plate gasket)
Cat monitor to be completed (cat is probably saw better days)
Next is changing valve cover gasket
showing photos of old spark plugs and box of the plugs I installed