(*) Re-Edited a little bit, pls reread

> I'd like to mention that I don't need more mic inputs, just more connectivity for gear
Therefore I said AD/DA converter and not Mic Preamp

> Would RME ADI-8 DS MKIII be a solution?
Yes but is a little over budget.

> Could you please explain to me the "Expand with an AD/DA converter through ADAT" solution?

You can use ADAT as digital connection between the two devices.
Your UFX has two ADAT ports.

Connect two TOSLINK cables if you use single speed 44.1/48 kHz
         UFX ADAT1 OUT -------------------> ADAT IN    ADI-8 DS MKIII
         UFX ADAT1    IN <------------------- ADAT OUT ADI-8 DS MKIII

Connect four TOSLINK cables if you use double speed 88.2/96 kHz
         UFX ADAT1 OUT -------------------> ADAT1 IN    ADI-8 DS MKIII
         UFX ADAT1    IN <------------------- ADAT1 OUT ADI-8 DS MKIII
         UFX ADAT2 OUT -------------------> ADAT2 IN    ADI-8 DS MKIII
         UFX ADAT2    IN <------------------- ADAT2 OUT ADI-8 DS MKIII

UFX as clock master, ADI-8 DS MKIII as clock slave.

Good TOSLINK cables are from MUTEC, because they are not so thick and the plugs fit well into the optical ports. You can also twist several cables a little to give it a little more structure, then you can use cable ties to stabilize this a little more every 1m. This way I got i.e. a nice 3 and 5m cable, consisting of 4 TOSLINK cables, between preamp and a RayDAT
https://www.thomann.de/de/mutec_optisches_kabel_1m.htm

According to standard a TOSLINK cable can be up to 10m long, with RME usually 15m are no issue but is over the standard.

(*) Therefore I mentioned UFX+ / MADI, it allows cabling between each of up to 8 devices in a MADI ring up to 2km (multimode) with single mode even 10km. Single mode needs special order. The new AVB + MADI capable devices use SFP ports, where you can plug an optical transceiver of your choice for MADI to support either multi or single mode. Needs the only a proper optical cable to support the one or the other standard.

A MADI based solution is more expensive (over budget), but I wanted to introduce you into this thematic, as you have advantages in terms of scalability (more channels (64)) and higher cable lengths than officially 10m for ADAT.