I'm messing around with F15T8 lamps in my Litemaster fixture, and if the bulb is on and I press the off button quickly, the lights starts to fade out like rapid start in reverse. You also see striations when doing it. The same effect also happens if you quickly press the on button when off.

It is electrodes cooling, so loosing the emission. Normally the electrodes are heated to just sufficient temperature for the emission. When you interrupt the current even for a brief period, the temperature drops, so does the emission. It drops so low, the related arc power is too low to reheat it again, so as it cools and the emission drops further down, so does the discharge current.
With the ON button it is the same - you warm the electrodes only slightly, so the arc can not hold on, but already some current flows so the lamp lights. And again, as it cools, the currents decreases, so does the brightness.

I messed with some 2x36 T8 luminaires that were miswired, as in - starters are crossed between the lamps. So the starter that starts lamp 1 heats the Phase (ballast is on Phase) end of lamp 1 and Neutral end of lamp 2

As long as both lamps are ok it sorta works, i guess the lamps are not preheated in the optimal times on the Neutral end (when starter 1 opens, it is unknown whether the Neutral end is hot or cold, as it depends on whatstarter 2 is doing)

When starter 2 is stuck, lamp 1 works (with the Neutral end still glowing in the working lamp) and Phase end of lamp 2 is glowing

Removing lamp 2 then stops Neutral end of lamp 1 preheating, but i have not seen effect on the brightess of lamp 1 when i turn lamp 2 to make or not make contact. Is it because in the working lamp the emission is limited by ballast current and not the electrode ?

... Is it because in the working lamp the emission is limited by ballast current and not the electrode ?

Yes, normally the arc heats up the electrode enough (it uses to settle for a 10..15V of the cathode fall). When you add external heating, you may decrease the cathode fall by few volts (to about 7..10V), but that is practically no difference when speaking about the consequent arc current (so the brightness).
The lamp fading is, when the current rises/falls around 5 to 10% of the rated current and when the current is limited by the available OCV (not enough voltage to cause emission by just high electric field; way easier to get on a 120V OCV than on a 230V, just because the same absolute voltage of the cathode fall is double in percentage on 120V, so impacts the current way more severely than on 230V).
Usually when you exceed about 30% of the rated current, usually the amount of generated heat on the cathodes is sufficient to make the system "flip" into the normal hot electrode operation. For less than 10% it usually dies out (10% current means 100..150V cathode fall for the same heating power, that starts to be too much even for the 230V).

These figures are even the base on how the RS starts: Very tiny capacitive glow, then as the electrodes warm up so they support about the 10..20% of the rated current means the lamp gets gradually brighter to that 10..20% level. That goes as fast, as the cathodes are warmed up by the heater winding, so the gradual (few seconds) fade-in is quite well visible. At that point the cathode fall gets enough power to provide way higher heating power, so the further warmup gets way faster, till the current became limited by the ballast. The last section is rather fast, so shows rather immediate (fraction of a second) increase in the brightness from the 20% to full ballast power.

I also noticed that while on, if you press the off button for about 1 second, you can actually sustain this glow, but if some kind of electrical contact is made, it starts to fade out.