There’s a few things to be aware of here. The route cause is that your web browser is probably holding the audio driver so that Cubase can’t ‘get it back’ again, so to speak.
So, ideally you need an audio interface who’s ASIO driver is multi-client. Many if not most are that i’ve tried. Are you running from a dedicated interface? If you’re running ASIO4ALL you can actually open the control panel and see which ports are available for the ASIO driver that Cubase uses - you will notice that when the browser takes a port it will have a red cross on the ASIO4ALL control panel for example. Only way to get it back is to close the app and eventually ASIO4ALL will take it back.
If you’re not using ASIO4ALL and have an audio interface with ASIO driver, then the other common issue is if the default windows sample rate differs to what you’re trying to run in Cubase - keep those the same where possible.
If you reply, list your Audio Interface (if any) you’re using, and whether it’s the manufacturer ASIO driver or ASIO4ALL, please.
On my main desktop machine i have an audio interface and have no problems whatsoever, i can run Cubase audio AND something like YouTube simultaneously.
On my laptop using it’s onboard sound running through ASIO4ALL - it’s just a pain, especially as the laptop speakers are addressed separately from the headphone. Sometimes i can get sound from my headphone output, but Chrome has hold of my laptop speaker outputs!
Never had any issues like this when i used to run on a Macbook. Microsoft still lag behind when it comes to audio drivers - but they have a far wider array of hardware to keep compatible.