If on job sites OSHA is important, but your company should require that one (maybe worth asking)

There are ACI certified things that could be useful. The field sampling or anchors would be my recommendation but also use your judgement on what meets what you do.
https://www.concrete.org/certification/certificati...

Of course, the PE is paramount. Look into taking the test early (more and more states are allowing this now) or going to California and getting your PE early. Studying and test-taking are easier while you're fresh out of school, and have fewer "life" concerns like young kids.

OSHA 10 has some value, as I recall LEED and PMP are tough to obtain without years of experience.

But I'd argue that in construction engineering, the biggest thing is exposure to different project types and resources. Page through the California FW manual, NAVFAC, ASCE 37 and the rebar cage stability guide. Even if you are tied up on one specific project day-to-day, look through old projects your company has worked on to see how they've detailed this type of brace, or what kinds of jacks they used there. You want to be absorbing information so that you can pull it out of the memory banks when everyone's scratching their heads about a new problem.

And of course, get as much field time as you can.

For field guys, office guys, and even design guys I'd recommend getting a special inspection cert from ICC and maybe the concrete field testing technician from ACI (link that Eric posted above). Even if you don't use it, it'll force you to learn a lot of the construction rules and tolerances required for the various trades. I got my masonry cert when I was an EIT. Never used it and let it lapse when I became a licensed engineer but learned all the rules about grout pour vs grout lift, tolerances, storing block, erecting block, etc. The kind of stuff they never teach you in school and you don't use on an everyday basis in a design office but everyone from engineer to contractor to subcontractor is supposed to know and be doing, at least in theory.

LEED and NICET

For the most part, nobody is going to care what certs an EIT holds. When you get a PE, that trumps the certs.

You'd probably get a better ROI spending your spare time to doing something fun.