Looking for advice on what to do with $130k liquid after closing on our home

My wife and I are closing on our new home on 12/31. We bring home about $11,400 a month. Once we’re in the house, all our monthly expenses (mortgage, utilities, food, general spending, etc.) will be around $6,300.

After closing, we’ll have roughly $130k in liquid cash. We both contribute regularly to a 401k and Roth IRA, so retirement accounts are already part of the plan.

Here’s what I think we want to do, but I’d love some feedback:
• Keep around $50k in a HYSA as an emergency fund.
• Put about $40k into long-term investments targeting ~7% returns.
• That leaves another $40k I’m not totally sure about.

We put 20% down on the house because we plan to refinance or throw a lump sum at the principal a few years down the road if rates drop.

So the question is: What’s the smartest move for that remaining $40k? Should we keep more cash? Invest it? Put some toward the mortgage anyway? Something else?

Just looking for some straightforward opinions on the best mix between safety, flexibility, and growth.

Thanks in advance!