And from the Pee rated superstar, who can be found in row 1 of Mystery Theater 3000, Science and physics are not outdated, unless you are a student of the strong force affecting quarks and gluons.
At least half of the advice is trying to help you find a better manner of thinking about the problem. That is not outdated, but often ignored. And I was the person who suggested you print out, study and highlight the last 4 years, @Roark (who has his own problems, thinking that “Punisher” = Cthulhu, but who will never be nearly as scary as the original) just suggested you look it over.
Anything that pertains to equipment that you have abandoned is outdated.
Now here is an answer to your question. First, and I think you’re OK on this, you should not confuse a combined DAC/AMP with separates. You need to think Digital source > DAC > AMP > Headphones. If you want to go down a rabbit hole, you can think of cables, but don’t.
This pattern from source to headphones (or your ears, and brain after headphones) will have certain synergies. Improvements or changes to one part will affect how you perceive or how the rest of the path works. Nobody hear likes to give simple answers, because we always think of this synergy. Obviously if the recording is bad and the rest of the chain is great, it will expose how bad the recording is.
Now I’ll give the simple answer. Headphones are most important. Probably should be about half of your budget. The complex thing is that as you know, not all headphones work with all sources, and it pays to think first about your total budget and what you want to accomplish. Some headphones can work with many chains, others will be highly finicky and will only work well with some components. So it makes a big difference if you want to upgrade over time or buy all at once as to what your reasonable choices are.
SECOND would be the amp, or the AMP section of a DAC/AMP. This is because the top culprit for synergy is between the amp and the headphones. The safest amp is a relatively powerful solid state or tube hybrid amp. This style will work with more headphones than most others. After you outgrow a good amp in this category, you’ll be buying multiple amps for specific uses.
THIRD is the DAC, or DAC section of a combined DAC/AMP. This is way down the line. Unless you have the amp and headphone right, you probably won’t hear much difference between a $10 DAC and a $5000 DAC. However, if the HEADPHONE is properly resolving, and you have a decent amp, then you will hear differences. Your Dan Clark is capable of resolving differences. The things in a DAC that you hear will be detail, and soundstage first. Instruments will be placed more precisely and more easily identified. IMPORTANT (and impertinent) - You will have to TRAIN YOUR EARS AND HEARING to reliably detect this. I strongly suggest going to live music - especially small acoustic or lower volume jazz, folk, country, or chamber concerts to listen carefully to how it is supposed to sound.
I hope this is helpful to you.