A mini IP camera with POE (power-over-ethernet) and a wide-angle lens. The POE isn't strictly necessary (Wi-Fi works too) but you'll need a cable anyway to power the camera, so POE is convenient. Bluet.it uses a 5MP camera with infrared and a 1.7mm focal length. The bundled software is truly terrible (and Windows-only), but the camera supports the ONVIF protocol so it can be configured with other software.
With a POE camera you'll also need a POE injector. If your ethernet cable needs to bridge a long distance, choose one with enough voltage (the cable at Bluet.it is 40 metres).
The camera outputs an RTSP stream, which can't be embedded in a website directly. To convert an RTSP stream to a browser-compatible format you need a conversion step. You can use a commercial solution (in 2019 Pimpelme.es used IPCamLive), but now we use the excellent open-source Restreamer software. The conversion now runs locally in a container; the Docker host is an Intel NUC8i3BEK running Debian 12. Restreamer converts the RTSP stream with FFmpeg and also runs NGINX with a nice front-end for configuring and serving the stream.
Streaming over HTTPS is possible too, with several options. (1) Follow the Restreamer documentation, though it's quite brief. (2) Copy the host system's certificate into the Restreamer Docker (BYOC = Bring Your Own Certificate). Certbot can generate a certificate on the host system. (3) The currently active option on Bluet.it: configure Apache on the host as a reverse proxy for the Restreamer port, reusing the host's certificate without copying it into Docker. The advantage: when the host certificate auto-renews, it also covers the Restreamer.
If you want to record as well as watch live, a NAS is the easiest option. Bluet.it uses a Synology NAS running Surveillance Station, which handles event detection and records when motion is detected in the birdhouse.
A birdhouse suitable for blue tits, with enough internal space to mount the camera. The blue tits of Bluet.it live in the Portland birdhouse by Natuurpunt, also sold by AVEVE.