The phrase, "With everything going on," is a dependent clause; its sole purpose is to explain why the speaker's life is hectic at the moment. The speaker is describing his or her current situation (there is a lot happening at said moment in time) and why life is hectic/crazy. The current events are making life hectic/crazy. I hope this helps.

Everything going on - there is often something that is disruptive. For example, I have used ‘everything going on’ to refer to the busyness and disruptive ness of the year since COVID-19 began.

It means with all the things happening and events taking place currently.