How do you upgrade stats and potential?

The two materials do not do identical jobs. Star Sands and Star Essence both feed stat upgrades, but potential specifically runs on Star Essence. That makes Star Essence the material you feel the shortage of, because every point you pour into raw stats is Essence you no longer have for potential.

So treat them differently when you hoard. Star Sands has one use and can be spent freely on whatever you are levelling. Star Essence is the bottleneck, and if you are aiming at a particular Aniimo's potential, spending it on stat upgrades across your whole roster slows that down.

Where your Aniimo starts out

Upgrading is only half of it, because the number you begin with decides how much work is left. Umbrawl Aniimo, also called Umbra Aniimo, are guaranteed to have perfect potential stats, so there is nothing to fix on that front. For wild catches, spawn rates for Aniimo with 9/9 and 10/10 potential scores have been increased, which makes hunting for a good starting roll a more realistic plan than it sounds.

Adventure events are the other route. Certain ones, such as the Cross Tea Party, can raise an Aniimo's innate or Initial Potential, and that can happen up to four times. Four is the ceiling, so a low roll can be improved but not rebuilt through events alone.

Core skills are a separate upgrade

An Aniimo's core skill does not run on Star Essence or Star Sands. It takes a Prismatic Stone, and it can be upgraded exactly once to boost its effectiveness. There is no gradual investment here and no second attempt, so the choice is only about which Aniimo gets the stone.

Not settled: Potential upgrades lean on Star Essence specifically while stats draw on both materials, and how strictly the game holds that line is build-dependent.