Why is there a large "well-shaped" distortion when the input voltage exceeds the power rails of an op-amp?
You have exceeded the common mode range of the inputs. When you do so, the output voltage is undefined.
There is also &quot;inversion&quot; or &quot;phase reversal&quot;, and cannot easily be explained by simply looking at the schematic. It is, however, a well-known behavior- see, for example, this document.

Input Common Mode Range
The recommended common mode range is 0 V (relative to the negative supply) to VCC – 2 V over the full
temperature range. However, the actual upper common mode range varies by approximately 4 mV/°C,
with cold temperatures reducing the upper limit of the common mode voltage range.
Note that when used as a comparator, only one input needs to be within the common mode range. The
other input can be above the common mode range or above VCC and the output will be the expected VOH
level (for Vin+ &gt; Vin–) or VOL level (for Vin – &gt; Vin+). If both inputs exceed the upper common mode range,
the output is undefined; it could be either the VOL or VOH level and the result may vary part-to-part, lot-tolot, over process, over temperature, etc. If either input or both inputs are lower than –0.3 V with respect to
the negative supply, excessive input current can flow and the output may display phase reversal, also
called inversion.
Because the inputs have no internal diodes to VCC, the input voltage can exceed the VCC voltage. If this
occurs, the input will block current flow due to a reverse biased diode forming in the input PNP transistor.
Current flow is blocked even if VCC equals 0 V. If either input or both inputs exceed maximum the VCC
rating, junction breakdown can occur. This may lead to permanent device damage per the table notes in
the respective device's data sheet Absolute Maximum Ratings table.

Not all models adequately replicate that behavior, nor do they necessarily go wonky where the input common range is exceeded. At 25°C the input common mode range is at least to 4.5V with a 6V supply, and your model seems to misbehave at 4V in.
Also, in reality, applying a negative voltage relative to the &quot;GND&quot; pin directly to an input from a low impedance source can easily destroy the chip.