I tested the CPU usage of having a website open in Firefox in the background and leaving it idle for 10 minutes. No other applications were running except for a terminal emulator which was the selected window during the test.
Websites varied greatly in the amount of CPU used. Some particularly heinous sites use a huge chunk of CPU contantly and indefinitely until the site is closed.
This shows that simply having an inefficiently-designed website open in the background can drastically increase CPU load, leading to increased energy consumption/battery usage and less CPU resources for your other applications.
I ran this test on an older (2017ish) laptop running Linux Mint using only 2 running applications: Mozilla Firefox and the Kitty terminal emulator. To measure CPU usage, I used mpstat from the sysstat package.
Firefox had only one open tab which was used to load the website being tested. All browser extensions were disabled. All autoplay for both sound and video was disabled. Even though this reduces total CPU usage (significantly in some cases), I wanted to ensure a fair test where no audio or video was being played across all sites. I verified this for each site outside of the test conditions stated below. I was also not logged in to any of the sites while testing.