Your first sentence is indeed grammatical, but the second sentence is not.
If you had just checked, that act of checking occurred prior to another past event, and no such other past event is identified in this second sentence. (Of course, the other past event could be identified earlier in the same text.) But the use of Present Perfect in the second clause (haven't received) is ungrammatical here, because the Present Perfect needs to connect to the present, whereas your second sentence, with its Past Perfect first clause and the implied reference to a later--but still past--time, keeps everything connected in the past, not to the present.
The grammatically correct version of your second sentence would be I have just checked with the supplier and they still haven't received the contract.
Your first sentence is focused on the relationship between the 2 events in the past, and my revised version of the second is focused on the connection between the past event in the first clause and the present result/relevance in the second clause.