Now edited with information available through 5 March 2024.
Bells Hells leveled up to 12th midway through "Ruidus" (3x83). Here is what the various characters gained:
ORYM
Orym took a 12th level in Fighter and almost certainly used his ASI for the Tough feat, since his Hit Points jumped from 99 to 130. (He rolled a 5 with a +2 CON, getting him to 106, plus 2x12=24 points from the feat, totalling 130.) However, his INT also rose 1 point and he now can cast Hex, a 1st-level enchantment spell. The most likely explanation is that his deal with Nana Morri gave him the Fey Touched feat, which if correct means that he also can now cast Misty Step.
EDIT: As of "Doorways to Darker Depths" (3x86), Orym can also cast Misty Step, confirming Fey Touched.
EDIT2: Liam confirmed he took the Tough feat at Level 12 and received the Fey Touched feat as a result of his deal with Nana Morri on "4-Sided Dive: Feat Fetishes" (4SDx21).
FEARNE
Fearne continued her multi-class into Rogue, taking a 3rd level and choosing the Arcane Trickster archetype. This gives her access to the Wizard spell list, including Mage Hand plus two more cantrips, two 1st-level spells from the illusion and enchantment schools of magic, and one additional 1st-level from any school. So far, she's implied several times she now knows Disguise Self, a 1st level illusion.
EDIT: Not a part of leveling up, but Fearne revealed that the ability she got from the undead pirate captain allows her, as a reaction, to gain resistance to cold damage.
ASHTON
Ashton took their 12th level in the homebrewed Barbarian Path of Fundamental Chaos. This means they now have an additional Rage (5 total) plus an as-yet-unidentified feat.
EDIT: Ashton took the Savage Attacker feat. They rerolled the hammer's damage dice during the 3x84 battle, and then commented they were stuck with the damage roll on the second attack. Thanks to u/DustSnitch on Reddit for catching this.
EDIT2: On "4-Sided Dive: Feat Fetishes" (4SDx21), Taliesin said he took Great Weapon Master on "4-Sided Dive: Feat Fetishes" (4SDx21). However, it's very likely he misspoke, since he followed up by saying, "It means I can reroll ones or twos on my damage dice," and that is definitely not what Great Weapon Master does. Very likely he took the Fighting Initiate feat, with the Great Weapon Fighting option. Thanks to Kaymax93 for this suggestion.
CHETNEY
Since Chetney took a 1-level dip into Rogue, he's now at 11 Blood Hunter levels. This means he now can transform into hybrid form twice per short rest, and has access to Lycan Regeneration which gives him a 3 hit point boost (1+his CON modifier of 2) boost at the start of each turn if he's conscious but under half his hit points.
EDIT: Not part of leveling up per se, but Chetney as part of his deal with Nana Morri got the feat or ability Legendary Toymaker. In "Doorways to Darker Depths" (3x86), he used it to carve a toy.
EDIT 2: Travis revealed in "4-Sided Dive: Feat Fetishes" (4SDx21) that it takes one hour to carve a toy, and if it is picked up or handed to someone, they become entranced by it for 1d6 minutes.
FCG
Fresh Cut Grass continued taking Cleric levels, and apparently took a half-feat (a feat granting a 1 point increase in an ability score, plus some new ability) since their Wisdom increased one point to 18. However, there are SO many feats that could do this (Fey Touched, Observant, Resilient, Skill Expert, Telekinetic, Telepathic just for a start) that it's really hard to say at this point which one they took.
EDIT: FCG cast Misty Step again in 3x85, so Fey Touched is looking like the winner. It is still possible, however, that he cast the spell using the Staff of Dark Odyssey (since he's done that in earlier episodes) and his new feat is something else.
EDIT2: It's Fey Touched. The Divination spell he took is Identify. See "4-Sided Dive: Feat Fetishes" (4SDx21).
IMOGEN
As a 12th-level Sorcerer, Imogen took an as-yet-unidentified feat rather than an ASI, since her ability scores didn't change.
EDIT: As suggested by u/DustSnitch and u/alexweirdmouth on Reddit, Imogen almost certainly took Prodigy, although Skill Expert is a possibility if you accept her apparent lack of gaining a skill point is a result of correcting a prior error. However, based solely on what we know (i.e. she had no stat increase but has expertise now in Persuasion) Prodigy is the best fit. If so, she also got a tool proficiency and a language.
LAUDNA
Laudna opted to take this level in Sorcerer rather than Warlock, giving her 9 Sorcerer levels. She now has access to a 5th level spell slot, an additional sorcery point, and knows one more spell.
EDIT: The new spell she took is Animate Objects.
Anyone have any additional insights?