Salary negotiation help? [MA]

Received a job offer for $165K even though I had previously told them I’m looking for 200K. They asked what my bottom line was and I said $180K. They went silent after finding me too expensive and said they will be interviewing other candidates that align with their budget. They did not disqualify me just yet. The next day after sleeping on it I realized I really want this job and feared losing the offer. I went back to hiring manager and said “I’m willing to accept $165K”.

This apparently left a bad taste in the hiring managers mouth because apparently what was happening in the background without my knowledge was that the hiring manager was looking for ways to reallocate budget to accommodate my ask before receiving my message.

What the hiring manager may or may not know is that i communicated to the talent acquisition partner that I can only accept $165K if we can bake into the contract that we do an automatic salary increment to $180K after 6 months pending achieving my KPIs. Otherwise my bottom line is 180k

My question is if after concluding their interview with the other candidate and still decide to go with me, did I screw myself for “back pedaling”? How do I salvage the Situation and insist on my bottom line of $180K