How much does power amplifier really matter comparing to other hi-fi components?

As between pre- and power-amp, it's really a question of what kind of sound you like (warm, analytical, bassy, slightly rounded edges, etc.) and then carefully matching components, within your budget, to get that sound. You can combine a relatively expensive power amp that has a sound you like with a passive or very clean active power amp that is not very expensive. Or, you can spend more on a pre-amp that gives you the sound you like and less on a power amp that adds nothing but power to the sound. Personally, I'd rather have a pre-amp determining the sound and a very neutral power amp. These days I run a Parasound JC2 preamp ($4500 when not on sale) with a pair of VTV Purifi 1ET400A mono blocks (about $2000). Some folks prefer combining tube or hybrid preamps with solid state power amps. But instead of adding the distortion of tubes, I've just ordered a Schiit Lokius tone controller ($300), which allows me to tailor the sound to the peculiarities of specific recordings.

     Every component shares a slice of responsibility, when it comes to accurate sound reproduction (not to mention: room treatment).

     ie: Picture all of your components (sources, cables, pre/power amps and speakers) as panes of glass, through which you want to observe something living.

      The accuracy/enjoyment of your observations will be determined by how many and how dirty the panes.

       How critical you are as listener, will determine your level of involvement and investment.

I believe it’s a good percentage of your system and should be chosen per your speakers and their capacity. Don’t forget your power conditioner and monitor. I spent 500$ on one that insures it’s protection. 

Everything matters. Amp matters a lot. Recently I’ve owned 3 amps I can swap among in my system. Each has a very distinct sound. All 3 are way more than enough power (120 - 275 Watts / ch) for my 96dB Tannoys, so overhead & drive capabilities are not really a variable. I’m even writing down particular combinations of cartridge & amp that work best together lol.

You didn’t specify your budget!  I can’t believe all these people made recommendations without that info.  It matters because up to a certain level, you’d be better off with an integrated vs. separate power and pre.  An integrated will compromise on the preamp section, but save $ on an interconnect.