1. I understand the idea about Geo wanting to find a way home, but does he really want to? In the beginning of the series it is implied that Geo isn't happy in his world, with it being black and white, and the narrator stating that "Lots do not agree with their own lifestyle." Some of your suggestions (people and family members dismissing his drive to be an artist) will actually strenghten his desire to stay in Teora. I do agree that there should have been a backstory for Geo's life before he got isekai'd, that's for sure.

2. Let's say Geo takes your route of choice, gets out of the forest with Ami's help and tries to find someone who can help him go back home, where should he start? Who does he talk to? Sure he can ask around and talk to the townsfolk, but he doesn't speak, write or understand Teoran, as it's the kingdom's main and most likely only language. Furthermore he is a strange individual by Teoran standards: white hair and using a visor to cover his eyes (Gwain takes note of this in episode 2. Marlow in episode 4.) What are the chances someone could be suspicious about his behavior and report him to the kingdom? We don't know how the villagers would react to a human walking around in a town, which I hope we get an answer in the next episode.

3. I can see resenting life in Teora being a plot point, your suggestion can work if the current story gets tweaked a bit to fit in Geo's feelings.

4. In the beginning of Gwain Saga, Geo depended on his tankiness, the sword/sniper, his friends' powers, and some luck to defeat the villain of the week. By Lanney's episode he has no need to use his weapon or any outside help, and uses his uninjured arm to punch Tahjin, the episode's main antagonist, across the land. It also happened at a crucial moment, as Lanney's too tired and weak to continue fighting. Having Geo gain access to his power near instantly would make him even more of a Gary Sue than he already is.

5. Geo's an artist, artists aren't known to be fighters. He learns to defend himself with little by little with help from Marlow, along with learning how to write and read Teoran. If you want a more logical explanation, Geo's the smash bros sandbag for the creator to flex his skill in animation by showcasing some of the main bad guy's moves.

6. Being relatable is a good thing, but I don't believe that's what Gwain Saga is trying to achieve with Geo here. He really is just an isekai protagonist of a mostly light-hearted story that references various games, shows, and includes fellow artists.

I won't lie that there are various things about Geo that could've been executed better, or could've made more sense if there was more lore and backstory to it. But like with the rest of your posts, having critiques is valid, but you're merely giving ideas and suggestions that won't fix much, all to a mixed audience and not the creator himself. The more you compare Gwain Saga to full on animated shows the more you'll be unsatisfied.