Minimum wage in California seems to be $16 an hour. I doubt this intersection took 37 500 man-hours to finish, so I don't think the cost is explained by wages. Also, $200K would still seem like a gigantic amount of money for adding stop lights to a single intersection.
There's a proposal to redo a playground in San Mateo's central park—bids have come in around $16M.
https://www.cityofsanmateo.org/4142/Central-Park-Playground-...
It's a nice playground design for sure, but it's kind of amazing to consider what could be built privately for the same amount. You could literally build a palace on a giant estate with fancy landscaping, a swimming pool, tennis courts, movie theater, etc.
Of course there are reasons why public projects are more expensive, but it does seem pretty crazy on the surface.
You probably need an engineer. A couple. They might have to run traffic studies beforehand to estimate the design requirements and light timing. They might have to consider other network nodes beyond this in their modeling. They might have to also run studies afterward to retime the lights to meet realized demand.
I’m surprised its not a $6m project honestly.