You might need a bigger transformer, I can’t tel L what voltage it is other than 20va and it have 3 voltage outputs At 24v 16v and 8v the C is common for those 3 voltages.
20va is pretty weak at 16v it’s barely 1.25amp , probably won’t power up 2 camera and door bells.
Find out what total voltage amp requirements for your camera and door bell needs and over size it by at least 20% and get a new transformer.
I used a 24v one from hvac @40va off eBay for $10. but ymmv you know you and you do you situation.
If you need to test your current transformer.
Get a multimeter put in ac voltage mode, one probe to the C terminal and verify the corresponding terminal output the correct voltage.
Yes you have a chance of burning up a transformer by overloading. ( should clarify this, it should read your transformer could have go bad from overloading as well, troubleshooting starts with testing voltage output.)