Feeling embarrassed and stupid for thinking a man was flirting with me

I (60F) have been working for the past few months with a man (50ish) on some projects on a property I own. Over time, he has become what I thought was more flirtatious. He tells me how beautiful I am often ( though I really am just "OK" in the looks department.) He says how lovely my eyes and hair are, puts his hand on my back or takes my hand to guide me through the construction area. Yesterday he told me he wants to take me out to dinner and drinks at his favorite restaurant. I was flattered at this attention. I have not dated since before the pandemic, so it was very nice to hear these things from a handsome man, and I admit that I did do some very mild flirting back from time to time.

I mentioned this to my best friend, and she laughed and said I must be misinterpreting his actions because she knows he is actually married and his wife is beautiful, implying that he would never be attracted to someone like me. She said he was just trying to be nice, and that it was just me misunderstanding because he is from a different culture (Latin).

I am mortified. I feel like I have made a total fool of myself. That he and the other men are probably laughing at me behind my back. I have to work with him for a couple more months until this project is completed. I don't know what to do to mitigate embarrassment going forward.

Edit: Wow, thanks for all the replies. To be clear, I have no desire for or intention of getting involved with a married man.