Hello Hnparr4,
We don't want you missing out on audio from websites or from your videos, so let's get this figured out.
You have taken some great steps to isolate the issue by testing the alert sounds, and restarting. You can further isolate the issue by connecting headphones to see if the videos or websites have sound.
This resource may help: If you hear no sound or distorted sound from your iPhone, iPad, or iPod touch speaker
Since you can still hear alert sounds from the receiver, your bottom speaker may be blocked, so this section from the resource might help the most "Remove all screen protectors, films, or cases from your device. Check the speaker opening to see if it's blocked or dirty. On iPhone only, make sure that the receiver is not blocked or dirty. If necessary, clean the speaker or receiver opening with a small, soft-bristled brush. Make sure that the brush is clean and dry."
Please make sure your iPhone is backed up and running iOS 13.6: Update your iPhone, iPad, or iPod touch
Have a great day!