Applying for a credit card before building a home?

So about a year ago my wife and I got a pre-approval for a mortgage. My wife had an 806 Experian score and I had a 773 Transunion score at the time. My score is supposedly lower than hers because I don't have any credit cards or revolving debt like she has(I pay her credit cards off most of the time when she does use them ). I have a business credit card but that apparently doesn't affect my score. We only use credit cards for cash back and always pay the balances off every month.

In the next month or two we're going to start getting bids on the house we plan to build. At the earliest, it will be 3 months until we go to a bank to apply for a construction loan, realistically probably more like 4-5 months.

Would applying for a card now be a bad idea? Should I basically wait till after the house is built before getting one?

I want one so I can get an 800 score also (not the best reason). Wouldn't our current scores get us the best rate? I also just want to have more access to capital if I ever have an emergency. The capital after building will be a lot lower and access to capital never hurts, even if it's just a bridge to get to Roth money.