Streaming services are going to need an internet connection. Some cars have a built-in hotspot/Wi-Fi, or can have it added (independent cellular connection). Or your devices may use the iPhone hotspot, if your mobile service provider allows for that on your current plan (ask them on t&c and limits for TV streaming through hotspot before you unknowingly get billed for it separately.)
Screen Mirroring without Wi-Fi is peer-to-peer AirPlay, which doesn’t support outside connectivity, not cellular, no nothing. Only good for (DRM-free) offline/downloaded media. Nice gimmick from long ago, but these days everything wants internet connectivity.
You can use the HDMI connection (thus not need the Apple TV box), if you would use an iPhone to HDMI adapter. Those come in two flavors: Lighting-to-HDMI (for iPhone 14 or earlier), and USB-C-to-HDMI (for iPhone 15 or later).
Netflix has chosen to not support AirPlay of any kind since early 2019, which may or may not also affect other less-talked-about mirroring efforts (e.g. adapters).