Warning: Contains SPOILERS for His Dark Materials season 2, episode 2, "The Cave."
His Dark Materials season 2 has fixed the show's biggest problem with its daemons, as evidenced by the use of them in the first two episodes. In the world of His Dark Materials, daemons are the manifestation of a person's inner-self; although they appear and operate in a separate physical form, they are part of their human. Daemons are on of, if not the most important part of the universe created by author Philip Pullman, given how closely tied they are to their respective characters, and so it was a shame when His Dark Materials season 1 didn't quite get them right.
While the CGI for daemons in His Dark Materials season 1 was impressive, it was also used very sparingly. Whereas in the books daemons are everywhere, since everyone in Lyra's world is accompanied by their own one at all times, the show had to find a variety of excuses to keep them hidden: making more of them into smaller creatures; having them out of shot; or explaining that not everyone feels the need to have them on display all the time, and other such excuses. It was understandable for budgetary reasons, and didn't detract from the overall quality, but given how intrinsic they are to the appeal of His Dark Materials' world, it was a bit of a letdown.
With His Dark Materials season 2, the show has found a couple of fixes for its daemon problem. The first episode, "The City of Magpies", took viewers to the world of Cittàgazze, or the city in the sky. Although it has some similarities to Lyra's world, the humans there don't have any daemons. With the only other characters being Will Parry (who also doesn't have a daemon) and Lyra herself, then His Dark Materials didn't have to find a range of excuses for not having daemons on display constantly. This continued in season 2, episode 2, "The Cave", the majority of which was spent in Will's Oxford. Much like Cittàgazze, this is a world where people don't have daemons, so again it was very easy for the show to get away with not having as many of them on screen.
At the same time, though, His Dark Materials season 2 is making the most of this opportunity. Rather than having its main characters in daemon-less worlds and still having fewer daemons, the first two episodes manage to capitalize on it by showcasing a greater range. In the His Dark Materials season 2 premiere, Pantalaimon changes several times - this includes his familiar forms, such as the ermine, to being a wolverine, a bird, and a red panda, the latter of which is used again in episode 2. The second episode also has some more shots of the witches' daemons, including a couple of great close-ups, and likewise of Mrs. Coulter's golden monkey, and a few more of the Magisterium members' daemons are shown as well.
This has allowed His Dark Materials season 2 to find a balance with its daemons that it didn't have in season 1. His Dark Materials season 2 was largely filmed before the first had even released, and while there's obviously more that can be added in post-production, it does seem a more natural occurrence due to where the storyline goes, rather than a more direct attempt at fixing the problem, but it's worked out nonetheless. There are still a couple of telling moments - in episode 2, there's a scene where Pantalaimon is forced into a backpack because he's a daemon in Will's world, when it could perhaps have simply had him transform into a dog or other animal that would exist there. But Pan still emerges from the bag regularly, so it doesn't completely hide him away. There's room to grow for sure, but on the whole the daemons in His Dark Materials season 2 are already much better than before.