Not only are they mentioned but the Buddha also clearly stated that they exist when asked by someone in MN 100:
But Master Gotama, do gods absolutely exist?”
“I’ve understood the existence of gods in terms of causes."
“But Master Gotama, when asked ‘Do gods exist?’ why did you say that you have understood the existence of gods in terms of causes? If that’s the case, isn’t it a hollow lie?”
“When asked ‘Do gods exist’, whether you reply ‘Gods exist’ or ‘I’ve understood it in terms of causes’ a sensible person would come to the definite conclusion that gods exist.”
“But why didn’t you say that in the first place?”
“It’s widely agreed in the world that gods exist.”
The Buddha replies that he knows by experience that they exist. He didn’t say yes the first time because the questioner could have believed that he said yes because of hearsay rather than by personal experience.
And as you say they are omnipresent in the suttas. In the EBTs, they are as real as human beings.
PS: it’s worth reading Bhikkhu Bodhi translation which phrases it in a different way (without adding the ‘absolutely’).