I've heard about how whales have evolved to increase in size for the
purpose of obtaining more food.
Well, partially, but it's also for thermoregulatory purposes, and for defense against now-extinct "megatooth sharks" like the various Carcharocles species, Isurus hastalis and Hemipristis serra.
I've also read about the giant and
colossal squid, so it doesn't seem too outlandish for a squid to
evolve to the size of whales.
No, not all. Although it should be noted, there would still have to be some significant increase in size, as squids are not very dense for their length. For comparison, a giant squid can be as long as a humpback whale, but the largest recorded individual was a hundredth of a humpback's mass.
For locomotion, I'm thinking of elongating their mantles to allow them
to swim in the same manner as whales.
This I find unlikely. Modern cephalopods move using jet propulsion, sucking water in and expulsing it backwards through their siphons. Meanwhile, cetaceans move by undulating their spine up and down (because of their mammalian vertebrae - consider that mosasaurs and icthyosaurs had tail paddles which beat from side to side).
These are very, very different methods of locomotion, and the latter is very difficult without a flexible spine (a gladius wouldn't cut it). I'd advise you just have them use jet propulsion, perhaps beating their wings for extra boost.
As for feeding, I'm considering two main ideas. They are able to
repurpose their siphon to take in water, and then keep some sort of
baleen like mechanism that filters out krill, small fish, or whatever
else is small and form schools on my world.
This sounds a lot like the "baleen squids" of the Speculative Dinosaur Project. These animals (one of the greatest creative triumphs of the project) have two modified tentacles ending in a feather duster-like cluster of filaments which they use for filter-feeding.
I would recommend a filter-feeding lifestyle over your other idea. However, rather than copying the idea from the baleen squids, you should probably put your own spin on it. My suggestion is that they use their gills as baleen; if you look at a squid gill on an anatomy diagram, you could see how it could be repurposed as a filtering organ. This would also be consistent with your siphoning-in idea.
They play an important role in the ecosystem, similar to that of
whales, but more stable. They reproduce faster and are more fertile
when young. Instead of birthing single helpless calves, the create
long chains of eggs.
Sounds good. William J. Sanders actually linked the large brood size of sauropods to their large size; the more offspring you can have, the higher the reproductive rate. a high reproductive rate means that there's a reduced extinction risk, and thus an opportunity to grow large.
(Also, the more offspring you have, the smaller they will likely be - in other words, the more different they'll look from the adult form. This means that they'll probably undergo an ontogenetic niche shift, where the young occupy a different niche to the adults. This also reduces the risk of extinction.)
Does anything about this sound implausible? Let me know.
Except for the locomotion bit, it all checks out. Welcome to WB.SE, by the way.