I always have Windows File Explorer running when I’m working on projects, with it targeted at my current project’s project folder. I just let the mixes go to the Mixdown subfolder within that, and I can always just go to that subfolder in File Explorer and double click on a mixdown to play it with the default Windows media player to hear it on my computer speakers.
I do a lot of mixes in the course of a project, and I change the name at each level, for example “SongName, Demo Mix 1”, “SongName, Work Mix 2”, …, “SongName, Rough Mix 5”, …, “SongName, Mix 8”, … When I get to just plain “Mix” as opposed to qualified mix names, it means it is a final mix candidate. I may have multiple generations of mixes in each category, depending when I reach some milestone where I want something to listen to in order to gauge the overall progress, compare to reference track, take a listen in the car, or whatever. I keep the Mixdown folder sorted in reverse date order (i.e. newest first), so it is easy to see what is the latest, but I can also go back to earlier iterations if, for example, I want to see if I really have progressed things with the most recent tweaks.
When I get to project archival (which will be outside the working project folder), all the mixes other than the final one will be in an “old mixes” subfolder of the folder were I have my main mix, karaoke mix, and instrumental mix in different formats (most typically CD quality, 24-bit 48 kHz, and 24-bit 96 kHz, in addition to various MP3 versions for specific purposes).
With File Explorer, if I need to switch back and forth between the project folder itself (and there will be CPR files in that folder with names similar to the mixes in the Mixdown subfolder), I can always just open another tab to be able to easily switch back and forth between the project and mixdown folders, but I rarely need to do that.
Of course, if you want to listen to the mix in Cubase, you can always use the capability to create a new track with the results after exporting, but it’s rare for me to do that unless commit submixes I want to use at some point in the mixdown (most typical one would be a background vocals submix, which I used to do a lot for performance reasons on my older computer, but rarely need to do on my current system, though I sometimes may want to do it just for organization).
With respect to file names matching Mixdown names, one reason I keep File Explorer up all the time is because, after any significant milestone (e.g. tracking lead vocals, tracking some specific instrumental part, comping some part, …), after saving the project, I copy the CPR file to a meaningful name. And, as I do each mixdown, I do the same thing. I’m also using the MixConsole snapshots in that way, including making comments in the notes field on what I changed. Of course, that runs out of snapshots after the 10th mix, but I just delete older snapshots. (I don’t think I’ve ever used the snapshots for actually restoring an earlier mix, but the history helps me keep track of things while I’m working on the project.)
If I’m using something other than the Windows player to play a mix, the Mixdown folder is also useful for quickly finding the file I want to use. The most frequent programs I use in this respect are iZotope RX (using the feature that lets you preview what various streaming environments will do to the mix) and WaveLab (which I often use to compare to reference mixes toward the end of a project, and in which I have multiple listening configurations set up, for example to listen through different environment simulators and view what’s going on in multiple analysis plugins).
I also use the Cubase project structure for daily backups of anything that has been changed that day. I’m just doing that manually since there are only a few directories, and the reverse date sort makes it easy to see what’s been updated.
When I finish a project, I do all the alternate mixes, stems, etc., unmastered mixes, etc., just letting that stuff go to the Mixdown folder initially. Then I move the relevant files to the directories I use for preparing the archives. I also use the Project/Backup facility to create a stripped down copy of the project at its final mix stage in that directory after removing all the extraneous stuff that is no longer part of the project.