I can give you my view - I would buy an old road bike and slap a brand new groupset on it. Neo retro is the way to go for me, there are many excellent old road bikes around and steel...is real!

You will probably fit in your budget if you also sell your current bike or sell the old parts from your new one. I see Shimano 105 R7000 groupset for 600$ in US websites.

I find such a project worth it because you quickly learn everything about bike mechanics, you are involved in it personally and as a result its not just a random bike you picked up at the store.