Does connecting Hue Bridge to HA, disconnect itself from Hue servers/app?

I’m sorry if this was asked before but I couldn’t find anything on searching/google.

But as title says, I’ve connected my Hue Bridge to Home Assistant, but it doesn’t seem to connect to the Hue Servers/App. And on Hue Bridge the 3rd light for internet access is off. I’m debugging so just wanted to confirm if it’s due to me connecting to HA or issue with the hub.

All three lights should be on. Did you press the button on top of the bridge?

It should work fine with both. Mine is connected to HA via the integration and is able to access internet (for updates) just fine.

I use mine with all the options simultaneous.
It is a hue Bridge V2 (the square one).