I recently tendered my resignation at my current company (senior engineer; get along well with the teams, but my boss's boss promised big bonuses and raises they never delivered even when my team delivered on-schedule and under-budget). I was offered several counter-offers but declined since I don't trust management anymore, and pretty much all managers became hostile to me when they realized I'm not staying (I'm one of three critical employees in a certain area, and one is on maternity leave).
My employer has been trying to determine who my new employer is (not a direct competitor, but it's a large fortune 500 company that buys expensive things from my current employer on occasion). My employer has been trying to get me to sign these very lengthy non-compete agreements (that list about 30 companies viewed as "competitors", and have blanket clauses like "we can decide at any time who we deem to be a competitor").
I'm not signing anything, and managers from work (including some people I previously thought to be friends) are trying to join my LinkedIn profile and asking (repeatedly) about where I'm going. After swearing at one obnoxious/persistent manager who was messaging me via LinkedIn (and un-friending them; they were calling me "unprofessional" for not updating my profile with the new employer's name, just my job title instead), I get a call from my boss who stated that the company will make a point of taking legal action against me if they discover who my new employer is and they don't like it. I tried to be courteous and told him "oh, don't worry, it's not our industry, just another company who could use my skills in automation". The reply was "we can prevent you from working on automation tasks as per your non-compete: the industry doesn't matter".
Question: Should I just never update my LinkedIn profile for the next year or two (i.e. so my soon-to-be-ex-employer doesn't figure out where I'm going). This is stressing me out, and I don't have the money for a drawn-out legal battle.