EVAP cannister fuel drainage, codes P2419, P043E, P043F, P2401 and P2402?

Hi, I recently saw a thread about a Toyota that was throwing out codes relating to the EVAP system failure. An expert said the problem could stem from overfilling the fuel tank causing the canister filter to become filled with gas.

My question is, will the fuel drain out of the canister filter as the amount of fuel in the gas tank gets lower or does the filter have to drain manually somehow?

My car, listed above, is throwing out 5 codes (P2419, P043E, P043F, P2401, P2402) also here's a video of the scan:

https://imgur.com/gallery/bJ4sDEV

I saw an expert recommend starting with a new gas cap. My current gas cap seems to fit snugly, but long ago the tether broke and I've dropped it a lot so maybe it's been damaged). Anyways I plan to start with a new cap, clear the codes and only fill up half a tank at a time for a couple weeks to give the fuel a chance to drain out.

Any insight or advice with this problem is appreciated, thanks!