Generating a high speed single-ended voltage output from differential currents

...as far as i have read about them (also their data sheets), if an ADC has both single and differential ended inputs, we can use it as a single ended input ADC OR we can use it as a differential ended input ADC. Which means we cannot use it as both single and differential input at the same time.

This is not always true. For example, I have used ADS1015 on a couple of projects recently. On this chip, whenever you switch the channel being read you also have the option to switch between single-ended and differential measurement. (This is not an endorsement of this chip for your project. Just an example of a chip that doesn't have the limitation you thought was universal)

Furthermore, even if you had a device that had to be configured as single-ended or differential for all channels at the same time, nothing prevents you from using ground as one of the inputs to a differential channel. So you could just configure it as differential and move on with your design. The only thing you'd lose is the opportunity to use the 4th input pin for some other purpose.

Another option, if you plan to use external signal conditioning, you can do differential to single-ended conversion in the signal conditioning circuit, and your ADC will never know the signals are anything but single-ended. This essentially makes the amplifiers shown in your diagrams to be external devices rather than internal to the ADC chip (and add some filtering in their feedback networks to reduce noise).

Well, this is exactly what should happen ! The reason is as follows:

Your input signal is a sinewave between 0 - 2.5 V

I could also say that your input signal is a 1.25 V (2.5 V /2) DC voltage + a sinewave with an amplitude of 1.25 V.

The thing that confuses you is the 1.25 V DC ! It is converted to differential as well, resulting in the DC voltages you see at the outputs.

If you want to prevent this you need to make that DC voltage at the input 0 V. This might be impractical.

Fortunately what you can also do is shift the DC reference voltage of the single to differential converter. I see that is has a Vocm input, if this is a common-mode level input then you could apply 1.25 V DC to it (the DC voltage I mentioned above) then the single to differential converter will consider 1.25 V as the commonmode level and the outputs will get the same DC voltage.