Warning: Word wall. TL;DR at the end.
It depends on what faction you’re playing (and playing against) really. Pre-expansion I would say resource management was much more prominent due to the fact that most factions did not really have great “refill your hand” cards. The fact that the new draw cards come so much earlier in the curve also really makes card advantage more irrelevant in the current meta.
Probably the most heinous offender right now I would say is Trinity Oath. Typically, even with draw cards like this card advantage is still important because casting a draw spell is usually going to be tempo-negative and possibly downright fatal depending on the board state.
But Trinity Oath is only four mana and was ironically given to the faction that can abuse it the most. The mana cost allows for Tempo Lyonar’s overstated minions to also come down the same turn you play it. Slo being zero mana means Trinity Oath is a decent play even on curve with no board. Compare it to something like Heaven’s Eclipse: HE comes out one mana later in the game, the only card that can be played with it on curve is Juxtaposition (which is typically useless with no board), and even on six or seven mana you can be left with nothing to do at times. Also, all of that doesn’t even cover the healing aspect of Trinity Oath.
Then you’ve of course got the faction that laughs at card advantage, Magmar. I don’t even bother worrying about managing my resources when playing against Starhorn now. Pre-patch Starhorn’s BBS let you use your cards more superfluously but now you might as well try to play as many cards as possible vs. him. In this kind of matchup, resource management is pretty much completely pointless.
Every other faction I’d say it’s an important aspect. Vanar, even though they were given a cantrip, still has no good in-faction way to refill their hands. Playing something like L’Kian is a huge tempo loss most of the time. Spelljammers, Sojourners, etc. can actually be denied unlike a lot of the new draw cards. Vetruvian is largely unchanged here as well, as Divine Spark really doesn’t see much play.
Songhai has to worry even more about resource management now as they got even more burn spells (the “top-tier” Reva list runs nine different cards for draw and still runs out of cards sometimes). Abyssian still has Rite, I guess, but thanks to the bump in mana cost to six awhile ago it’s basically skipping a turn unless you play it on 8+ mana at which the most impactful card you can play alongside it is Daemonic Lure.
tl;dr: Even though these big draw cards exist, most of them are fine. Resource management is still important even if you do run these cards as 1. There’s no guarantee that you’ll draw them and 2. Most of them are tempo negative, so forcing your opponent to use them can be advantageous to you. Is it less important than before? I think so, but it’s only significantly noticeable in the Lyonar and Magmar match ups.