If you want to observe an anglerfish safely, there is a scaled down, baby anglerfish held in the Observatory. It is also possible to lure an anglerfish far enough out of Dark Bramble that it is possible to see it clearly.
Anglerfish appear to be attracted by sound, including a collision between the ship and an object within Dark Bramble. They will growl after detecting the player and slowly move toward them. Using this mechanic, the player can lure an anglerfish to the edge of Dark Bramble in relative safety.
Sending your ship on a collision course towards an anglerfish (sticking a probe onto the angler would help track it) and then getting out of your ship and then moving away from it, the anglerfish will then attack your ship, but because the anglerfish spins (or lunges) towards it, it will destroy your ship and then spin wildly and out of control. at this point you would normally be dead so you wouldn't be able to see this happen, but since you are alive, you can follow it and watch it (it will no longer attack you). At some point the spinning anglerfish would then drift into space, and for a brief moment, you will be able to see it clearly (if you are close to it) but after leaving the planet, the anglerfish model will disappear and become an invisible entity, which you can still interact with as you can bump into it and hurt yourself.