Early Stage Career Uncertainty

I've tried to keep it short and to the point.

I am a fresher, a freshly minted MBA from one of the Tier-2 IIMs. Placed in a PE firm which I don't want to name out of fear of identification and retaliation. Had signed the offer letter and completed other formalities. 5 days before joining, they sent me a message via an intermediary (PC) that joining had been delayed by 3 months. From that point on, I have had a gut feeling that I should start searching and applying to other companies because I think that they will renege on the offer or change offer terms, due to their previous action and alleged workplace behaviours - company initially floated with a certain CTC and then upon selection, downgraded it by ~23.5%, saying that the quality of candidates is lacking (we negotiated via the said intermediary to meet in the middle and they agreed). Company is allegedly toxic, with their Glassdoor reviews largely in the extremes, either 1 or 5 stars, with the former pleas to not join, with sometimes in-office experiences and sometimes even mentioning people to watch out for whilst the latter being similarly worded reviews praising the company, which I feel could have been planted, although I do not have enough evidence to back that claim up. (I already knew about these reviews before applying too, yet I did it anyway considering the market conditions at the time)

What I ask of you is based on your large amount of work ex, certainly more than mine (0 yrs lol), I would like your opinion on this situation; whether can I apply and then sit for those processes in this period of 3 month delay and successfully change ships w/o any issues? (Note: Exact date has still not been communicated, just "3 months", even after multiple requests for a date via the intermediary.)