The rules of Familiars are as follows:
You gain the service of a familiar, a spirit that takes an animal form you choose: bat, cat, crab, frog (toad), hawk, Lizard, Octopus, owl, Poisonous Snake, fish (quipper), rat, raven, Sea Horse, Spider, or Weasel. Appearing in an unoccupied space within range, the familiar has the Statistics of the chosen form, though it is a Celestial, fey, or fiend (your choice) instead of a beast.
Your familiar acts independently of you, but it always obeys your commands. In Combat, it rolls its own Initiative and acts on its own turn. A familiar can't Attack, but it can take other Actions as normal.
When the familiar drops to 0 Hit Points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any Special Senses that the familiar has. During this time, you are deaf and blind with regard to your own Senses.
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons. Alternatively, you can dismiss it forever. As an action while it is temporarily dismissed, you can cause it to reappear in any unoccupied space within 30 feet of you.
You can't have more than one familiar at a time. If you cast this spell while you already have a familiar, you instead cause it to adopt a new form. Choose one of the forms from the above list. Your familiar transforms into the chosen creature.
Finally, when you Cast a Spell with a range of touch, your familiar can deliver the spell as if it had cast the spell. Your familiar must be within 100 feet of you, and it must use its Reaction to deliver the spell when you cast it. If the spell requires an Attack roll, you use your Attack modifier for the roll.
Nowhere in these rules does it say that your familiar vanishes every time you take a Long Rest. In fact, in standard tabletop D&D, players often have a familiar keep watch, as it is a magical creature and I make it so they don't need sleep. (Notice, nothing in the above rules says they need sleep, and they're magical constructs, not actual animals.)
So, I am suggesting to Larian that they do not make it so that Familiars and Animal Companions unsummon. They should not. You should be able to summon them on Day 1 when you crash on the beach, and if you are smart about them and keep them alive, you should be able to keep them with you the entire adventure without ever having to summon them again. Thus, on Day 2, you can have your Familiar in the party without using a spell slot to summon them, etc.
As for Animal Companions for Rangers and such, you either have one or you don't. Again, they shouldn't unsummon. You pick your companion, and they remain with you at all times until they die. You can't summon another animal companion unless you dismiss the one you have or it dies. Then and only then can you summon another - and you should have to wait for a Long Rest to summon another if the one with you presently died. If you dismissed it, you could summon another right away, but if it died, you should have to wait for at least a day to summon another. Call it grieving or just you not having another animal available right away - whatever - the point is that the penalty for it dying should be no companion for a day. Animal Companions for Rangers are friends, not magical construct pets, so you shouldn't just be able to summon them like magic spells.
I will say, however, I do like that you can just summon an Animal Companion rather than having to find one and charm it. Especially since there are no animals to charm, really, in the game. Although hunting for and charming an animal companion can be a mini-game of sorts, I'm not a fan of it. When I level up and become a Ranger Beastmaster, I'd like to get a pet immediately. I don't want to have to go hunting for one and then charm it and such like in some games. So that I very much appreciate.
Finally, Animal Companions should differ from Familiars in that they can fight and attack and such while Familiars are more for scouting and for channeling magic through them. Here's my suggestion for Familiars in BG3. In tabletop, the wizard can channel magic through the familiar if it has a range of touch. SOOOooooo, there aren't that many spells like that in BG3 that would really benefit the spellcaster. SOOOOooooo, I think it'd be really cool if the wizard could channel ALL spells that make sense through the Familiar. In other words, move the Familiar into range of Minthara, then Gale casts Magic Missile with Level 2 Spell Slot through the Familiar. Bam! Gale's way at the back, but the Familiar got up close and hurled Magic Missile. (Keeping in mind the Familiar must still be within 100 feet of the Mage for the Mage to channel through the familiar.)
Now THAT would be way cooler than letting them attack like regular animals, AND it would differentiate between them more effectively. Familiars would then be channels of magic power for Mages, and animals would be like companions and actual animals that fight by your side. Familiars would be good for getting in close so the wizard doesn't have to endanger themselves, while animals would be just like members of the party.
A Limit would have to be put on Familiars as channels, however, or they'd become OP. Maybe they can channel Level 2 or lower spells only. They couldn't cast Level 3 and higher, because then they'd be hurling fireballs and lightning bolts and that'd be too OP.
Though, I must say, that could be fun though.

Rendzer the Raven goes flying up to a higher level and Lynari, my Drow Mage, hurls fireballs down from Rendzer into a huge bunch of drow. Faboom! Bye bye drow.
Dang! Shouldn't give Larian such ideas. Now they'll implement it, and that's probably WAY too OP. WAY too OP. Right? RIIIiiiiiight?