Since this is Indian context:
Last week, senior project manager told me that "client has closed the requirement"
This is quite possible if the client didn't just close the position, but the contract as well (for your employer). Even otherwise, requirements for contract positions can be in flux depending on business scenarios.
On the other hand, recruiters can blindly cold call/email about opportunities just to get hold of your resume/contact details, so that they can pitch you another role which they actually have. So don't pay this too much attention. I've had incidences where recruiters reached out to me for the same role at the same company I was already working for, so never treat a middleman recruiter as source of truth.
I joined this company because I accepted their offer before other two companies sent in their offers. I am joining whichever company pays me more.
In my experience, the hiring process is broken, and offer shopping is very real in India. Even companies are aware of that, and few even plan for that (Hiring X+Y devs instead of the X devs they need because their past experience showed that Y in X devs don't turn up).
I've seen instances of companies being wary of presenting the proper offer letter, instead sharing offer details on plain text email so that they can get the candidate to actually resign, but not use their offers to shop further (doesn't work, but they try). Many a times candidates hold 4-5 offers before really joining the one they deem best.
As such, if you are really being undervalued, as per the market reality, you have the option of telling the company that you have received a better offer, and checking whether they can match your offer or not. In a competitive market, if the employee has to be competitive with skills, employers too have to be competitive with work environment and compensation. I have seen wide distribution of salaries for the same role with similar experience even in larger organizations, so negotiating doesn't hurt, though the way you negotiate might.
as I am hoping to get my one month's salary and one month's notice.
They are only going to pay you the amount mandated by your offer letter. Unless you have entered a messy organization which likes to renege on the offer letter terms (which would be against the local laws), they would be obligated to pay you. Going for the legal process can be very lengthy in India, so no point in burning any bridges.
Now, I have no interest in working in this company anymore. But I still want to know what went wrong.
Confront someone high enough in the food chain about it, but be polite when you do so. Since you have applied for a project manager role, in all probability you would have interacted with 2-3 other managers, or director. Ask them what they think happened wrong. Keep this informal (no written communication) and tell them that you ask because you want to understand if there was anything you could have done to get a more positive output.
As long as you ask out of genuine desire for self-satisfaction (yes, no fault of yours, but was there scope for being more proactive or get KT faster?), and not make it look like you are blaming someone/them/organization, people will not be defensive and will try to answer you professionally to the detail they can.
In my experience, HR in India can be completely clueless about the actual business decisions, and hence, other than reiterating templated responses, they are not a genuine source for understanding what went wrong.
My opinion based on your comments to another answer (IANAL): The company lost the position due to business reasons with the client. In the interest of self preservation of their own business, they have decided to let you bear the brunt of it, which is completely unethical. Since they have acted shady, they most probably will be (ab)using the clause of quick termination under X month probation period that most offer letters in India contain. If you have such a clause in your offer letter contract, do also check about the notice period pay in such case.