I've been messing around with a 35mm camera. I'm a big fan of the aesthetic but I find myself balking a bit at the cost of a roll of film.
Is there any faithful way of adding the film look to a photo taken on my phone? Maybe using a generative adversarial network like StyleGAN? I haven't been pleased with the filters I've seen so far.
Really Nice Images (reallyniceimages.com) are pretty good. They have an iPhone app and also Capture One and Lightroom/Photoshop profiles (which you can use also with Lightroom mobile).
You'll probably be better off getting a copy of Photoshop. There have been countless tutorials published on how to achieve this type of effect specifically over Photoshop's lifespan
I don't have the answer you want but I wanted to mention that the Fujifilm x100 35mm point and shoot camera has been flying off the shelves because it contains a number of film simulations that mimic classic fujifulm stock.
There are some photoshop add-ins that can add grain and some color correction. The Nik collection comes to mind. https://nikcollection.dxo.com