Pixel 8 Pro Notification problem?

I just switched from an iPhone to a Google Pixel 8 Pro and I'm not sure if this is a bug or is just something that I would have to mess with in the settings.

Sometimes I get a random vibration from my phone, which I would be expecting it being a notification, but I cannot find the notification in the drop-down menu.

Also, in my old iPhone, when I receive a notification while using the phone, I get a notification bubble dropping down from the top of my screen. On my pixel, it seems like this thing only appears when an action is needed such as approving a request. I would like it to also appear when I get notifications from emails and such, but I have no idea what is it called or where to find it in the settings.

So far I am very happy with my Pixel but I just cannot figure out how the notification works on this phone. It would be great if you guys could let me know where should I be looking for these settings.