Welcome Keelo :]
As for your purchase choices, I don't see how you messed up anything. Using the Topping as a pure DAC actually takes care of the potential downside it had with the upgrade (the headphone-out output impedance isn't something too great if you're using low impedance devices like many modern IEMs). So as a DAC you get all of its performance with none of the potential Frequency Response randomness that could occur using aforementioned low impedance headphones/IEMs.
Personally, I would only use high-gain on any device only if I feel I'm lacking in power for whatever reason. If I am maxing the volume, and it's still not high enough, that's when I would move to high gain. Otherwise I go fully low gain.
As for specific question about what you should do (whether to set the DAC in full out-put line-out DAC Mode so to speak) or to have it where you can change it's volume. I personally have mine set a -8.0dB (looking at performance graph that seems to be the general area where it's best performance is) and I leave it at that, leave my source (computer or whatever) at 100% volume, and then do all my volume changes with my amp (I use a 789 so we're similar from a performance perspective).
As for whether you "bottlenecked" your setup. Well, if we're purely technically speaking. Perhaps yes. But the differences at play here are not within some realm where you're going to be hearing something like that - at all -
There's a reason Amir used the DX3Pro as his daily driver until the SMSL M500 and DX7Pro released.
On a side note, I saw you talk about you listening spread between gaming and music. I really wish reviewers and generally people online would stop with this bullshit (I get triggered by this nonsense). There is no "music" audio and "gaming" audio quality suited for one device or the other. The only thing gaming devices do better than "audiophile" devices is they simply have more gaming related features like specific DSP profiles that simulate different sorts of sound profiles, like adding echo or reverb. Or they simply have their features merged (like all-in-one devices that function as a microphone input, and audio output). So all it is, is just convenience (in the same way a "gaming headphone" may be simply a headset with a microphone attached, and a volume knob on the headphone itself for convenience.
But in the end, there is no quality difference in terms of these devices when you compare them. To the contrary, many "gaming" devices skimp out on sound quality (this is much less of a problem in the modern day with performance being good for the majority of the population). So unless you're talking about factors those secondary features about "gaming" audio devices, there is no such thing as a device that is worse or better performance wise if you are seeking fidelity/transparency from the sound. Basically the question makes little sense to ask about gaming audio vs music audio (again, unless of course it's those other physical or software features I spoke about).