Electrical – n amplifier voltage limit for the input signal even if the differential voltage is small

The most common solution for your problem is to use an isolation amplifier such as Analog Devices AD210. Note that there are many different models available from many suppliers.

Isolation amplifiers are generally broken into two categories: 2-port & 3-port. The number of ports specifies how many isolated sections are in the amplifier. A 3-port isolation amplifier has the input separated from the output with both sections separated from the power supply input. A 2-port isolation amplifier has the power supply in the same section as either the input or output, depending on that particular model. Obviously, 2-port isloation amplifiers cost less than 3-port units.

Also be aware that the isolation voltage is different between ports. The AD210 that I mentioned earlier has higher isolation voltage rating between the input port and both other ports whereas the output port has a lower isolation voltage between itself and the power supply port.

A quick Google search for the search terms "isolation amplifier" will show you the plethora of options available.

Note also that I as speaking of Analog isolation amplifiers. If you have the ability to convert a digital bitstream into your desired result at the destination, there exists another plethora of digital isolation devices.

Does this effect depend on anything else than the JFET/BJT input stage?

Slewing can happen in any stage of an OpAmp, it can happen in the input stage, the output stage and any of the intermediary stages. It occurs whenever a capacitor is driven by a fixed current source. For a given configuration one stage sets the limit and determines the slew-rate often this is in fact the input stage.

A typical input stage consists of a differential pair with a tail current source. In equilibrium the current of the tail current source splits equally and when driven hard on transistor takes the whole current. The required voltage to turn one of the transistors (almost) off determines the onset of slewing. It's a fixed voltage for BJTs and a variable voltage for FETs.

If slewing happens in the output stage and the output stage is not symmetrical (e.g. class A) it is possible to have different slew-rates for falling and rising edges.

Are there input stages where an even lower differential input voltage leads to the maximum slew rate? Perhaps some sort of hybrid?

I don't know of any off-the-shelf devices that do this, but certainly there are adaptively biased OpAmps that increase the current through the input stage to improve the slewing behavior.

Even if there are only two types, do different op-amps of the same type (say, BJT) have different levels?

BJTs have a fixed level, unless emitter degeneration is used and FETs can have different levels.