Hello and welcome. I am glad you could find a way to use Midimix.
Unfortunately, Steinberg has not foreseen common convenient way to change presets. In old MIDI world, there was banks + programs. That is not brilliant from today's perspective, but at least something with 2 levels structure and standardized along all MIDI synths. That was not taken as the basis by Steinberg. They haven not prescribed how presets nor banks have to be switched. Some plug-ins have continued to use MIDI standard, but that is not common. In addition, Steinberg has "killed" almost all MIDI extended features, including this one, in VST3 (related messages are no longer delivered to plug-ins, at least not directly).
Cakewalk still use one flat list of presets, which you can see on the top bar of any VST/VSTi (there is no technical difference between them). And the only possibility from surface is to load "next" or "previous" preset from the list. More or less working combination in AZ Controller for that:
* ACT R1
* Function Context Open
* Command "Increment(Decrement) Plugin Preset"
In practice, almost all plug-in was forced to "invent own wheel" for plug-in preset management. Obviously that is not standardized and so host controllers can't work with that universal way (some plug-ins allow MIDI assignments, other expose that as automation parameters, yet another category try to use VST build-in presets concept and so presets are exposed in the presets list, finally most plug-ins support preset loading by mouse only).
No wonder NI Komplete Kontrol and Akai VIP are so popular now. Controlling parameters was the same for decades (a part of Cakewalk ACT, Novation Automap, etc.), but preset (and plug-in) management is what make these "micro hosts" convenient and allow deep hardware integration (for own hardware only... they have learned from Apple that selling dedicated hardware and giving the software free/cheap is way more profitable then selling software for any hardware).