The UCX has no Sample Rate converter in Hardware, so it can only be clock master or clock slave.

For operational reasons I prefer to have the recording interface as clock master, which is connected to the PC and has TM FX routing capabilities. Because then the Application (DAW, MusicPlayer) can set the clock rate for a project. And then the UCX and all other digitally connected interfaces behind the UCX learn sample rate automatically from the clock master.

So if you would connect now an ADI-2 Pro/DAC to the UCX via ADAT, then it will receive the clock from the master via ADAT, but then because of SteadyClock it would refresh the clock and for its own D/A conversion it would use finally its own internal FS clock.

FS delivers measurable but not audible better results. FS is simply being chosen for newer devices, because FS clocks are now available for a better price than in the past (because it's available, not because it's necessarily needed for better sound or quality).

Along with the ADI-2 Pro I think that it started that the term "SteadyClock III" was introduced. Most likely because the FS clocks are now there in some products. But as it doesn't seem to be audible from what I read here in this forum, its at the end of the day more or less irrelevant.

If you have an UCX as clock master and an ADI-2 Pro or DAC it will simply work... No reason to be worried in any way.
And if you connect your monitors and phones to the ADI-2 Pro / DAC behind the UCX, then digital audio would be D/A converted anyway with the internal FS clock, even if UCX is master, because Steadyclock receives the clock, refreshes it internall and D/A conversion takes place with its own (FS) clock.

Please read this information: https://www.rme-audio.de/steadyclock-fs.html
and the technical section in the manual, here from your UCX:

38.3 Digital
• Clocks: Internal, SPDIF In, ADAT In, word clock in
• Low Jitter Design: < 1 ns in PLL mode, all inputs
• Internal clock: 800 ps Jitter, Random Spread Spectrum
• Jitter suppression of external clocks: > 30 dB (2.4 kHz)
• Effective clock jitter influence on AD and DA conversion: near zero
• PLL ensures zero dropout, even at more than 100 ns jitter
• Digital Bitclock PLL for trouble-free varispeed ADAT operation
• Supported sample rates: 28 kHz up to 200 kHz