Dunno if useful, but in RC hobby area we have had OSD (on-screen displays) for decades. Both in analog and digital video, with recording (analog OSD there's just a small chip). Although analog is probably not relevant for you -- quality is crap and you don't care about milliseconds latency as we do, so go with digital (and not HDZero, they are technically digital, but heavily invested in low-latency, for pro racers).

Just don't buy DJI -- they absolutely want lock you in to their tools, parts are often not compatible even within DJI, require to create an online account, require an app (from a custom .apk on android) and in general have questionable privacy.

Of the open-source systems there's a new OpenIPC system with a most popular implementation of RunCam WifiLink 2 that supports onboard SD card recording [1] [2].

More proprietary (but still cross-compatible with others) is Walksnail Avatar V2 [3] with 32GB of internal storage.

For your case, you don't need a VRX (receiver), although you can totally give it your your buddies to see your race (with OSD) in real time. VRX can be built-in to goggles (if the same company), or as a separate module that connects to your preferred goggles over mini-HDMI, also with recording. [4] [5]

[1] https://www.youtube.com/watch?v=BP7Ns7H9wvI&t=49s

[2] https://shop.runcam.com/action-camera-categorie/

[3] https://www.caddxfpv.com/products/walksnail-avatar-hd-kit-v2

[4] https://shop.runcam.com/runcam-wifilink-rx/

[5] https://www.caddxfpv.com/products/walksnail-avatar-fpv-vrx-o...