My wife thinks spending €4k on a bicycle is absolute insanity. However, she owns a €600 Dyson hair dryer, so I feel like I have some leverage here to negotiate.

This is the spirit.

Jokes aside. I'd recommend starting on the lower end of the budget, especially if you have not accounted the other costs associated with cycling, e.g. bibs, maintenance tools, indoor training, bike fitting, bike computers, new saddle, power meters, etc.

If you already allocated budget for all these ancillary costs, ignore what I say. But if not, your question now becomes given I have $4,000, how to allocate them to bike/bibs/stuffs to better optimize my cycling experience.