Will a lender be able to tell what type of mortgages I have from looking at my credit report?

About three months ago, I purchased a home using my VA loan. The VA only does primary residence. I am trying to purchase another home now using an FHA loan which also only does primary residence. When the lender looks at my credit report, could they see it is a VA loan and know I just purchased a primary? Thanks in advance
How could this be considered fraud? I have not withheld any information they asked me. I answered everything truthfully
I know they will see the mortgage on my report. But how will it show? From what I have seen before it list the payment amount, history, balance, and lender information. Doesn’t list the type of loan that was taken out.

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