Can we use sentence transformers to embed sentences without labels?
The link you provided of Siamese Bert is an instance of a Bert or Roberta finetuned on STS or NLI data. Which can have the format sentence 1 is similar 3 out of 5 to sentence 2 (STS). Hence, is supervised, it does not fit your purpose.
Nonetheless, do not despair, there are some that do not require training, although may not perform as good as the supervised one. The below use word embeddings which you can train on your data corpora to generate sentence embeddings:

Word Mower's Distance
Sentence Embedding S3E

Or by feeding just sentences line by line:

DeCLUTR
Sent2Vec

P.S. I have not tried all of the solutions, to my knowledge I suggest these, cause either they are quite known or are quite recent.