There’s a nice cluster of suttas regarding characteristics of a sotapanna and what they cannot do at AN6.89-95, e.g.
After giving up six things you can become accomplished in view. What six? Identity view, doubt, misapprehension of precepts and observances, and forms of greed, hate, and delusion that lead to rebirth in places of loss. After giving up these six things you can become accomplished in view.”
“Mendicants, these six things can’t be done. What six? A person accomplished in view can’t live disrespectful and irreverent toward the Teacher, the teaching, the Saṅgha, or the training. They can’t establish their belief on unreliable grounds. And they can’t generate an eighth rebirth. These are the six things that can’t be done.”
“Mendicants, these six things can’t be done. What six? A person accomplished in view can’t take conditions to be permanent, happiness, or self. They can’t do deeds with fixed result in the next life. They can’t fall back on purification through noisy, superstitious rites. They can’t seek outside of the Buddhist community for those worthy of religious donations. These are the six things that can’t be done.”
“Mendicants, these six things can’t be done. What six? A person accomplished in view can’t murder their mother or father or a perfected one. They can’t maliciously shed the blood of the Realized One. They can’t cause a schism in the Saṅgha. They can’t acknowledge another teacher. These are the six things that can’t be done.”
“Mendicants, these six things can’t be done. What six? A person accomplished in view can’t fall back on the idea that pleasure and pain are made by oneself, or that they’re made by another, or that they’re made by both. Nor can they fall back on the idea that pleasure and pain arise by chance, not made by oneself, by another, or by both. Why is that? It is because a person accomplished in view has clearly seen causes and the phenomena that arise from causes. These are the six things that can’t be done.”
There’s more like that in MN115:
“It’s when a mendicant understands: ‘It’s impossible for a person accomplished in view to take any condition as permanent. That is not possible. But it’s possible for an ordinary person to take some condition as permanent. That is possible.’ They understand: ‘It’s impossible for a person accomplished in view to take any condition as pleasant. But it’s possible for an ordinary person to take some condition as pleasant.’ They understand: ‘It’s impossible for a person accomplished in view to take anything as self. But it’s possible for an ordinary person to take something as self.’
They understand: ‘It’s impossible for a person accomplished in view to murder their mother. But it’s possible for an ordinary person to murder their mother.’ They understand: ‘It’s impossible for a person accomplished in view to murder their father … or murder a perfected one. But it’s possible for an ordinary person to murder their father … or a perfected one.’ They understand: ‘It’s impossible for a person accomplished in view to injure a Realized One with malicious intent. But it’s possible for an ordinary person to injure a Realized One with malicious intent.’ They understand: ‘It’s impossible for a person accomplished in view to cause a schism in the Saṅgha. But it’s possible for an ordinary person to cause a schism in the Saṅgha.’ They understand: ‘It’s impossible for a person accomplished in view to acknowledge another teacher. But it’s possible for an ordinary person to acknowledge another teacher.’
I suppose, in the SN, there are many references to insight into Dependent Origination (DO) as a characteristic, e.g. in SN12.27 (mirroring the bit about insight into causes and phenomena earlier) when talking about the conditions of DO:
“When, bhikkhus, a noble disciple thus understands the condition; thus understands the origin of the condition; thus understands the cessation of the condition; thus understands the way leading to the cessation of the condition, he is then called a noble disciple who is accomplished in view, accomplished in vision, who has arrived at this true Dhamma, who sees this true Dhamma, who possesses a trainee’s knowledge, a trainee’s true knowledge, who has entered the stream of the Dhamma, a noble one with penetrative wisdom, one who stands squarely before the door to the Deathless.”
I suppose later stages on the path, including arahant, being technically still also stream-enterers, will share these characteristics.