I don’t see how there’s any useful synergy to obtain by mixing them.
You'd be surprised lol. Ime, i tend to see things like this in the way that traditionally shamans would see admixture plants with Ayahuasca. Aya seems to be a lot about synergy, and can teach you alot about other plants and what things do in the body, so if you mix certain plants with the Aya, even a few different plants in combination, they can work in synergy and provide other benefits that you wouldn't get from a basic Aya brew. I myself am always mixing different things with at least Harmalas to add some other benefits to the mix, or to take away certain side-effects, i haven't found there to be much risk at all, if any, so long as you don't mix the wrong things lol.
As for this combination, i haven't really gotten into medicinal/edible mushrooms yet, i have tried Lions Mane for a few weeks when i ordered some from Paul Stamets site one time, i didn't take it with the Rue but i did take it on days i took the Rue, but at the time had a lot of other things going on so couldn't tell if the Lions Mane did anything or not. But medicinal/edible mushrooms with Aya in my view definitely wouldn't present any risks, afaik there's nothing those mushrooms would do that would be contraindicated with say the MAO-A inhibition for example.
The thing i've found to be most noticeable when mixing things with Aya (particularly with DMT included) is that some things may "get in the way" of the DMT portion, but can go just fine with the Harmala portion, so i'm more on the lookout for what may interfere, because so far i haven't found anything to be particularly risky, though i would recommend steering clear of anything that potently inhibits reuptake of Serotonin for example, or say heavy doses of stimulants or something (due to the Noradrenaline), but other than that i don't think there's much out there that will truly negatively interact with Aya, to me Aya seems extremely safe and nowhere near as risky pharmacologically-speaking as people tend to think.
I for one say go for it and try the combo out, i can't think of any reason one should avoid it, but idk if there'd be any benefit to it, but as an admixture-loving guy, i'd say it's worth the experimentation to see what all different things may do in combination with Aya (with or without DMT), because there's so much potential there depending on what is in the mix, we can have many different "flavors" and variations of Aya for different purposes.
But yeah as far as having a mindblowing experience goes, just Aya will be enough, admixtures are optional and experimental.