I also took a look again at the AoE-book and there was also the note that inverting amplifiers dont suffer from CMRR-problems. But i couldnt find a description how supply bootstrapping (like done in the Fluke 5700A Page 542 with the LTC1052 https://xdevs.com/doc/Fluke/5700a/5700A_old_sm.pdf ) affects CMRR, only that bootstrapping allows the use of low supply OPs (with its sometimes better specs) while allowing bigger voltage input/output-swings.
Is it because CM-voltage is related to the middle of the supply voltages and always follows the input signal, so that the CM-voltage is constant?
Effectively it is although I do not know if it is specifically defined that way. If the supply voltages follow the signal at the non-inverting input, then it is just as if the operational amplifier has no common mode input voltage change.
If the common mode input voltage is fixed and the positive supply voltage is changed, then the positive power supply rejection ratio (+PSRR) applies. If only the negative supply voltage is changed, then the negative power supply rejection ratio (-PSRR) applies. If both supplies are fixed in value but shift together, then the CMRR applies.
Bootstrapping the supply voltages is easy enough and adds the common mode rejection ratio of the amplifier and the bootstrap circuit together. (1) This could be done to achieve the 140dB or higher CMRR needed in this application while using a non-chopper CMOS or JFET input operational amplifier for even lower input current and lower broadband noise at the expense of increased 1/f noise which is probably what matters in this application. Chopper stabilized operational amplifiers have flat 1/f noise making them especially suited for low noise DC applications. Broadband noise is easy to filter out so there is no reason to minimize it. Electrometer applications do not have a choice and have to put up with the greater drift and 1/f noise of a JFET or CMOS device.
Ive read that diodes, which are illuminated to generate a minimal current, could be used to cancel the remaining bias current. Are there any existing designs which use this concept?
Photodiodes are not required for that and I think they would be a bad choice. There are a couple of ways to implement fixed or adjustable bias current cancellation externally using diodes or transistors or even a second operational amplifier of the same type. I have never seen this done though for a chopper stabilized operational amplifier.
(1) It adds the separate common mode rejection ratios in dB. As a fraction or ratio, they multiply.