This is what I read.
Using the AD7193 data sheet from (https://www.analog.com/media/en/technical-documentation/data-sheets/AD7193.pdf),
On page 36:
Continuous Conversion Mode. Continuous conversion is the default power-up mode. The AD7193 converts continuously, and the RDY bit in the status register goes low each time a conversion is complete. If CS is low, the DOUT/RDY line also goes low when a conversion is
completed.
The chart on page 11 describes the CS pin as:
"Chip Select Input. This is an active low logic input used to select the ADC. CS can be used to select the ADC in systems with more than one device on the serial bus....." .
Page 34 also has a similar description of using the CS pin where several components are connected to the serial bus.
"CS is used to select a device. It can be used to decode the AD7193 in systems where several components are connected to the serial bus".
You can also look at the Timing Characteristic section. page 9, it does seem to show the DOUT/RDY signal going inactive/tristate with the CS pin going high.
The chart on page 8 lists the timing of T1 and T5 (as marked on the timing diagram), which are the delay times from where CS changes to where the active/inactive points of the DOUT/RDY signal begin. There may just be a 10nS delay on the DOUT/RDY pin after the CS returns high, (they call it "Bus relinquish time").
So it would seem that connecting other data devices on the same bus is a legitimate thing to do regardless of the operating mode.
While is is true that the data sheet does not literally say the pins are tri-stated, the only way the statement about having multiple devices on the same data bus could be acceptable would be to have those common pins tri-stated when the chip is unselected.
Of course if you still have doubts you could call the tech support at Analog Devices. The tech support link is at the bottom of the first page of the data sheet.