Hue Log can connect to a Philips Hue Bridge v1 (the first generation bridge, with a round shape) but many features and data will be missing. For example, the event stream which allow Hue Log to collect events from your system is not available. You can still see your Configuration and Capabilities, among a few other things.
The v1 bridge is no longer supported by Philips and as of April 30, 2020 Philips terminated support for their online service, including that software updates are no longer available.
This does mean that you will always have the third light blinking on the bridge, because it doesn't reach the internet (technically, it does reach the internet but not the Hue online service) and can only connect to it locally (that is why it still does work with Hue Log). You can also not use it with the offical Philips Hue mobile application, since it does require the bridge to be on the latest software version.
Since the v1 bridge cannot communicate with the internet, the auto-discovery will not work. Hence you need to connect the v1 bridge to Hue Log by manually entering its IP-address. But unfortunately you can't get the IP-address in the official Philips Hue app, so the best bet is to check the admin interface of your router to see which IP-address it assigned to the bridge.