How can I seriously calibrate ADC voltage readings with Arduino Nano?
Rather than mapping to a range of 0 to 4.4 V, map to the range 0 to 1.1 V and use analogReference(INTERNAL) to select the internal band-gap 1.1 V reference source.  This reference voltage might vary a small amount as Vcc varies, but the variation is likely to be just a few millivolts.

To get your input voltage into the range  0 to 1.1 V, use a voltage divider and a voltage subtractor.  The voltage divider ratio should map the 8-volt range of 22 to 30 V to a 1.1 V range, ie, should have a ratio of 8:1.1, and should map 30 V to 4.125 V and 22 V to 3.025 V.

If you use a Unity Gain Differential Amplifier as described at electronics-tutorials.ws, the divider can use large resistors, ie, need not provide the under-10 KΩ resistance needed for ADC input; instead, the UGDA's low output impedance will meet that requirement when used as ADC input.  For example, you could have 1 MΩ in series with 160 KΩ for the main divider.

Feed that divided voltage into V1 in the diagram below.  Use a pot or another voltage divider to create a 3.025 V reference to feed into V2, perhaps based on the board's 3.3 V regulator output.

Note, use R1 = R2 = R3 = R4, with all of them some value like 10 KΩ or 20 KΩ.