Which type of test tube should not be used for blood collection?
Your reasoning is sound and correct. The answer key is wrong.

An unclotted blood sample needs something to prevent clotting. Extracellular calcium is required for both the coagulation cascade and platelet activation. It even has its own name in this context, Factor IV. This why EDTA, a calcium chelator, is used in some blood collection tubes to delay clotting.

So, as you say, the most correct answer would be (1): Test tube containing calcium bicarbonate. That is the opposite of the kind of tube you should use for this type of sample.

The answer given by the key, (3): Test tube containing heparin, is incorrect. Heparin tubes are a good choice for plasma and whole blood analysis, as you indicated. Heparin is a good anticoagulant, both in vitro and in vivo.

See this nicely laid out list from UCI medical school for an example of specimen requirements for specific tubes.