350eur seems a quite overpriced, and you can probably get a very decent mirrorless DSLR at that price range, which means interchangeable lens etc. And it won't necessarily be much larger depending on the lens.

For example:

https://www.ebay.ie/p/Sony%2DAlpha%2DA5100%2D24%2D3MP%2DDigital%2DSLR%2DCamera%2DBlack%2DKit%2Dwith%2DE%2DPZ%2DOSS%2D16%2D50mm%2DLens/219510002?iid=276805429375

If you only ever want to do selfies and close photos, stick to your camera phone, convenience will almost always make it a better option. Just make sure your happy with the image quality (some camera phone photos are extremely aggressively processed, and it can look terrible on a larger screen). If you occasionally want to be able to get a better quality photo, or want a gateway drug to photography, something like the a5100 above is a good complement to your phone.

Edit: the a5100 screen turns right around, which makes it more usable for selfies than the camera you were looking at.

Edit2: I can see the response on Lemmy. World, and sopuli.XYZ, but not my home instance, so responding here:

I saw a photo on wikipedia, that showed the screen stopping at 90°, but if it goes to 180, looks pretty much the same.

You mention that your partner has an a6000, if I were in your position, I would just use that whenever the camera phone doesn't cut it. If its too bulky to carry around, then the a5100 is a bit smaller, but not significantly. Maybe a smaller lens and a small camera bag for the a6000 might make it more usable?