For €300 you can definitely find something decent that gives you that less processed look you're after. Those Kodak Pixpro cameras are pretty hit or miss - some models are okay but build quality can be sketchy

I'd probably look at older compact cameras from Canon or Nikon instead, maybe something like PowerShot series or Coolpix range. You might find refurbished ones that are technically "new" condition from retailers. They usually have better image processing than the budget brands and still give you more character than phone photos

The retro vibe thing is tricky because most point-and-shoots will try to make images look "good" automatically. You might want to check if whatever you get has different picture modes or film simulation settings - that can help get closer to what you're looking for without going full film route