Finding the 'weakest link' when upgrading?

Being able to find the weakest link when upgrading is really, really important.
Otherwise a different new component may never really be able to show how it is better. Since the other ’weak’ component(s) is(are) masking the new components better sound.

This is a difficult problem.

My best example is not exactly about the least sound quality, but it may show something about it.
I upgraded a good portion of my equipment all at once when I retired. And I still had in my system an old DAC I bought used. When I received most of the new components (including new preamp, new amp, new speakers and a new turntable and cartridge), I was comparing my old DAC with the new one. And found no sonic difference. I mean I tried every way I could and could not hear any difference between them/ So either I just wasted $25,000 for nothing or?? I was very frustrated.
Anyway, after three weeks I got another new bit which had to be ordered and built
.
When I plugged in the phono box, an epiphany and a flood ot tears.. My $25,000 of new equipment really was better. Since the phono box sounded glorious, thus it made it clear all the rest of the system WAS NOT holding back the new DAC. That new DAC was actually just not any better than my old one. And I returned it.

And unless I just happened to acquire that new phono box a week later, I would have been stumped why the new DAC (which was praised to the skies by both Stereophile and TAS) was not doing better.
I was seriously bummed and confused about wasting a ton of money... until I played the new phono box.

Now it was kind of odd that the two DACs, one, used for $250 )it’ original list price was $1,000) and the other $2,400 and 12 years newer) could sound so alike. But chance happened. (And toss in the official guru magazine praise with it all)
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Anyway, how do we find the right part to upgrade? Since making the wrong choice can leave one in the same boat I was in back in my example? (at least until I got the phono box)

I do not have an answer. and I ask.. does anyone?
For me it is just kind of a sixth sense, with little real science to it.

In general I have been kind of lucky.
But how do I know I have managed well?

I do not know.
It has been better more often than not.
(Though I have made a few really terrible choices over many years now and then. Costly choices)

Anyway, my question is how do you make the choice of what to upgrade?
How do you know or decide which is you weakest component?

And do you agree finding the weakest component is really important in the path of upgrading, or one might be making expensive mistakes buying gear, or trying gear? (which may really be great, yet you cannot hear it due to some other weak links in the chain? And though I hate to say so, this weak link may even be cables, or powercords or even the AC from the wall*.

*(but please do not get into a big theory arguments about interconnects and powercords and power conditioners.) Stick to the main topic of knowing how to find the weakest link.