I'm going to Azerbaijan and will be entering on an e-visa. Would I get the entry stamp in the passport, the visa sheet, or both?
This travel agency website has a link to a sample e-visa, which includes no space for entry/exit stamps. In addition, it mentions in the text that one should "make sure that you have free page in your passport". From this information, it can be reasonably inferred that your passport will be stamped upon entry.
In addition, this similar site suggests that to register with the migration service you will need a copy of the passport page with your entry stamp. Although this may not apply to e-visas, this is not mentioned and also points towards your passport being stamped.