In the process of TCP 3-Way Handshake, we can see this diagram often.

We can notice that the client socket state changes to [established] after received the 2nd packet.

What happens if the 3rd packet (client ACK) is missing?

in client:

int client_fd=connect(a,b);

Does connect() return after the 2nd packet is received?

What if the 2nd packet is missing? Does the server keep sending SYN-SENT packets?

And why does the server need to receive the 3rd packet before changing state to [established]? Why not change state to [established] after receiving the 1st packet?

I have been programming for a few years now, but I cannot understand this.

[update1:]——————————————–

thanks to all.
accroding to @user4581301，Andrew Henle，
I open https://www.ietf.org/rfc/rfc793.txt [Page 22] ， https://datatracker.ietf.org/doc/html/rfc9293#name-state-machine-overview [3.3.2. State Machine Overview]

and with @user207421 says,

My understanding is :
we call the 3-way paket,say packet1[CLIENT-SYN],packet2[SERVER-ACK-SYN],packet3[CLIENT-ACK]

1. both CLIENT and SERVER send A SYN,and need to recive A ACK,then the sock state can change to [established],so [3-way] is need
2. in tcp,not just retransmittion arise after [established],but also the 3-WAY itself will retransmittion after a packet timeout.
   every [seq=x] should waiting a [ACK,ack=x],or the [seq=x] will arise retransmittion.

I will study this rfc more.
I want to konw,
1.how to know the detail lays in rfc doc,on old days,I jus search google and reding some blog and article?
2.does stackoverflow is a good place to ask this kind quesion？