Talk to your pet like you’d talk to another human. You would not walk out of the house without saying a word if your partner or child was in the same room, or likely even in the house. You’d tell them you’re leaving and maybe even for how long and what you’re doing. Tell your pet:

Some pets have baggage (separation anxiety). So logically even though you always come back home they worry. This could be due to past experiences or just their nervous personality.
You don’t have to go into tons of detail. Outline the basics. You should not make a big deal of leaving just like you would not make a big deal of leaving your partner to go to the grocery store.
When you get home, greet your pet, and tell your pet how much you appreciate their loyalty of waiting for you.
Our pets are the only ones that would wait for all of eternity for us. Their loyalty is unwavering. And there is no time limit for them. They would spend every day of their entire lives waiting for us to return. So please tell them when you are leaving and when to expect you back.
All they want is to be with us all day every day. Even the ones without separation anxiety.
I can hear the animals but we can all talk to the animals, everyone, including you.