"This field cannot be used because it is computed" Please help me find a way to select formula field

That can't be fixed I'm afraid, you can't modify the contents of a computed field directly.  It seems like you're trying to store a date value, so you'll need to create a new Date field and point your automation at that

Your "Record ID" field is also set up incorrectly and needs to be an Airtable record ID like so:

Thank you so much for replying, but is there really no conceivable way to make it so that if I check the checkbox, the dates in the formula field will be updated onto the dates on the "start working on posts field"

I ran into the same thing yesterday. My workaround was to remove the Formula Field and write a script that updated a new Field based on "xyz" criteria. Then when I checked the box, I could run the script to update the remaining fields.

The only downside is that I have to make sure that I run the script after making a change on the table (like checking a box)! 

Yeap, select the 'Start working on posts' field in the 'Update record' action and use the value from the 'date completed' field