Switch – Replacing an old light switch with a new one. Trying to figure out correct wiring

Assuming that all 4 switches go directly to 4 different lights. Each light has to have a hot switch leg and a nuetral. In the switch box there has to be a branch circuit consisting of a hot wire (if Romex, the black wire) and a nuetral wire (if Romex, the white wire). All the light fixtures will have two wires comming into the switch box. Hook all the whites together along with the feed nuetral from the branch circuit. Hook one side of each light switch screw to to the branch circuit Hot wire. Hook the other side of the each light switch screw to the wire that goes to one of the four light fixtures. Looking at your smart switch it looks like it needs a nuetral hooked to the white wire and the two blacks are for the hot wire from the branch circuit and the other black is a switch leg that goes to which ever light fixture you are trying to control with the smart switch.

Alter the wiring to your left switch only slightly so it resembles this diagram:

Currently, your left switch has both the "power in" and "power to next switch" screwed to a common terminal. Add the "pig tail" and twist them together with a wire nut.

Now you can replace that switch with your timer where your "pigtail" is essentially your new power in. Your timer will likely need to be pigtailed to neutral as well.