Doubt between first bit sent to first bit received and last bit sent to last bit received transmission

So, in Patterson's Data Communication textbook, I was solving some numericals related to transmission delay and stuff of that kind. I get that transmission delay is the time taken by a station to "put" its data on the link(I assume, wire). But do we encounter transmission delay at destination site as well ie., does it take time to "unload" the data from the wire back to the destination station.

Related to this, shouldn't total delay for first bit sent to first bit received be equal to (1transmission time) + (1propagation time) for a link between station A and B. Consequently, the total delay from first bit sent to last bit received should be=(2transmission time) + (1propagation time) taking the extra transmission time on destination site?

Is it correct or did I make some mistake conceptualising it because regardless of asking such questions which are concerned about first bit and last bit sending in the textbook, the official solution manual for this book uses a single transmission time formula for every question. Please help.

does it take time to "unload" the data from the wire back to the destination station.?

No. I think you're mis-understanding the concept of transmission delay. Bits don't "wait" at the receiver until all are received before being processed. Once the receiver "has" all the bits, it has "received" the message (we ignore whatever the receiver may do with the message).

Consider a system where there is no delay -- `Tprop` is zero. When I send a bit, it is instantly received by the receiver.

If the first bit is sent at T0, the receiver receives it at T0. The second bit is sent (and received) at T1. Bit N is sent and received at Tn. So the total time is Tn-T0. i.e. Transmission delay.

Consequently, the total delay from first bit sent to last bit received should be=(2transmission time) + (1propagation time) taking the extra transmission time on destination site?

That is a common misconception. That textbook uses transmission delay for serialization delay but I find that ambiguous. Try to visualize single bits:

The first bit starts off (pretty much) instantly and takes propagation delay across the channel to be received. The last bit starts off serialization delay later, also takes propagation delay across the channel where it is received. So, the total for first-bit-out-to-last-bit-in is propagation delay + serialization delay (plus processing delay until the data can actually be used for anything).