How do dual output in waveform generators make sense
Then looks like the two outputs cannot ever be separate or parallel.

They share their return, or -ve, or GND connections. It's likely that you can put them in parallel, as they probably have a defined 50Ω output impedance. If for some unlikely reason they are zero output impedance, then you could use a resistor in series on each output before you combine them in parallel.

And, what should I do when I wish to connect the two signals in a series? Connecting CH1+ and CH2+ to the rest of the circuit?

You don't. Just like you wouldn't get two mains plugs, and say 'I have 240 V coming out of each, can I put them in series?' The two sources share their negative terminal, you would short-circuit the 'lower' source if you tried.
However, have you noticed, they are already in series, joined by their -ve or GND connections. Invert the sense of one output, and take the combined series output from the two +ve connections.

It looks like the ability of the dual output is too restricted, and the schematics looks really weird, all because of the grounding...

It's only too restricted if that's what you want to do. Most of us don't, at least for 99% of use cases for such a generator.

Am I somewhere wrong?

No, you're just having unwarranted expectations dashed. You will get over it.

Or ...Should I float the waveform generator and find another point in the circuit to explicitly ground the entire circuit?

Generally not. It depends what you're trying to do. It's not going to fix the two sources having a common ground.
Generally we would avoid lifting the ground of test gear, both from a safety point of view, and because doing so tends not to leave the instrument as isolated from ground as you would want, what with capacitance from the power supply to the case.
What we tend to do is one or more of ...
a) reconfigure the experiment so that grounded sources will work
b) synthesise a floating source with opamps
c) use a signal transformer to float the source
d) use the differential output to put them in series
e) buy a self-contained battery operated source