You're supposed to check if an update will interfere with your current app usage and decline the update, if necessary. That's what the update prompt is for: you're able to decline.
You chose to update, so you took the responsibility to make the updated app work with your environment. No app developer is able to ensure compatibility with every other app in the world throughout all releases.
In your case, OBS wasn't able to listen on the Websocket port:
Code:
20:53:01.089: [obs-websocket] [obs_module_post_load] WebSocket server is enabled, starting...
20:53:01.089: [obs-websocket] [WebSocketServer::Start] Not locked to IPv4 bindings
20:53:01.089: [obs-websocket] [WebSocketServer::Start] Listen failed: Only one usage of each socket address (protocol/network address/port) is normally permitted.
That's only connected with the Droidcam plugin if both plugins use the same port. You can change the Websocket port in Tools > Websocket server settings > Server Port. The default is 4455.
Reinstalling the Droidcam plugin made you restart OBS, so it may be the port was freed on later starts. However, to find the root cause you need to make sure no other plugin or app is listening on the Websocket port.