In previous publications there has been some mention of what an Awakened tree may do if you first shape them into anything that is both really large and made of wood. But what about beasts? You make them average intelligence anthropomorphically speaking and... then what? What is their lifestyle? What motives would they eventually have? What would they do with the rest of their lives?
Tasha's Cauldron adds magical zones to D&D world-building with weird 'storms' that can cause every beast within the area to spontaneously get more clever. Specifically, when Psychic Resonance (page 160) occurs there is a six percent chance all beasts gain that 10 intelligence if they didn't have it already. Such creatures also gain two languages and the ability to speak.
There are some creatures in the Monster Manual that have the Innate Spellcasting trait - they cast them without material components (or their cost). This will still mean an eight hour casting time. Note that dragons have optional rules for spell casting and they can choose nearly any spell (they would need to be CR 15+ for Awaken &/or Reincarnation).
Fortunately, they have lots of options if you look at beast ability scores. For example, a simple deer has an average score of 14 wisdom (some could be much wiser!) - that's about as wise as most low level druids, clerics and other religious monsters. They live short lives though - a mouse lives 5-7 years, a deer lives only 6-14 years. They need some serious solutions else their new-found brilliance will end... and soon! Unlike trees that naturally live for centuries, most beasts won't get far past a decade unless they happen to be an elephant or turtle.
The good news is, magic is very keen to add time to a creature's life. They may find time shifting in the Fae realms that allow them to live much longer or even stop aging completely - though this puts you at the hands and mercy of the locals. They may research a version of Reincarnation that works on beasts (especially if a god helps out).
If a beast were to gain a second form they would live much longer. If they had the druid's ability to change into a longer lived creature they would adopt the 'new' life-span. Obviously, a rabbit could live as an ancient clam for five centuries - but that seems weird.
If a beast can gain a human(oid) shape they can gain much more lifespan. Getting a human shape can bring them to 80+ years, getting an elven shape would mean a thousand. Also: elves are naturally druidic in nature - they are the most logical and plot consistent choice. Would getting the druid shape shift allow for an 'elven' form? Rules As Written it is not written down so it would need a house ruling.
If you are okay with light house ruling, an animal could also come down with lycanthropy 'curse'. In 5e the shapes already include suidae, canine, corvid, felidae, ursidae and more. It is possible that the right mix of magic and enchantment-research could yield a spare humanoid shape - giving many of these creatures the luxury of opposable thumbs.
