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Please join for a month, take leave on medical grounds for the next month and quit.

Two benefits: (i) you may actually like the job and would reconsider the reasons why didn't want to join in the first place and (ii) two months salary (in case you quit).
It depends if you're joining another firm or taking up another career option. Chances of anything happening in the latter case are less.
Law firms have much better things to do than sue lowly associates for breach. If the partner is nasty they will just make sure their network knows what a bad candidate you are. Its a reputational risk more than anything else.
What are the repercussions of not joining a firm after signing the engagement letter keeping the ethical considerations aside?