The orthodox Theravada interpretation is that he went through all four stages.
[I]n the course of his long wanderings in samsāra, the bodhisatta had been to all the realms except the five suddhāvāsa realms which are meant only for those who have attained anāgāmi stage. The bodhisatta usually attains all the four stages on the path only in his last existence....
But what is the attainment of path? How would one describe rightly the
attainment of the path?
The path to nibbana has four steps as you mentioned stream entry, once returner, non returner, arhatship. As you have asked How would one describe rightly the attainment of the path? I'll answer to that as below.
What is Stream Entry
When someone achieved this ...
It appears in many sutta of many nikāya.
Sutta Pitaka Vol 1 : Sutta. Tī. Sī Mahālisuttaṃ:
‘And what, Sir, may those other things be?’
‘In the first place, Mahāli, a brother by the complete destruction of the Three Bonds (the Delusions of self, Doubt, and Trust in the efficacy of good works and ceremonies) becomes a converted man, one who cannot ...
This might be the definition (it is, at least, one of the places where it's defined):
"In the Dhamma thus well-proclaimed by me — clear, open, evident, stripped of rags — those monks who have abandoned the three fetters, with the attenuation of passion, aversion, & delusion, are all once-returners who, on returning only one more time to this world, ...
Depending on our freedom from delusions, we can recognize conditions of equal or lesser purity.
It's like looking through glass: if other's glass is dirtier, you can see that, but if it's cleaner, your own dirt doesn't allow to recognize that.
Also, it's not possible to get consensus among practitioners, because many of them have delusions and misrepresent ...