There's two parts to your question: (1) "Where does my passaggio end?" and (2) "What's going on when I sing up to E5 like this?"
(1) Unfortunately, there's a lot of disagreement in the terminology and classification of the vocal registers, especially in the male voice. Some vocalists don't even really consider passaggio to be a real thing, since your vocal cords are either vibrating modally or they're not (I consider it to at least be a useful mental classification in some contexts).
The most useful thing I can say is that by your first recording, your voice is clearly naturally breaking into falsetto/head voice right at A4. This is about what I would expect of a high tenor. I have modal voice one full tone higher, and that's a little unusual. True countertenor voices have modal voices a good bit higher than that, but that's extremely rare.
One thing to pay particular attention to is the two notes around the point you tend to naturally flip into falsetto, G4 and A4. Those will tend to be your trouble notes. You have a little play with exactly where that switch happens, and preventing a flip (or flipping early) is an extremely useful technique to master to help keep those notes from feeling tentative.
(2) When you sing up to an E5, it sounds like you're attempting to force chest voice. It also sounds like you're hurting yourself. Instead of trying to sing that high in chest voice (you may be technically capable of forcing it, but it's a very, very bad idea), try to develop a fuller head voice. A true light tenor flips between the two effortlessly, often nearly unnoticeably.
If you want to gain a little more useful modal range or more solid head voice, and you're singing a contemporary style, ask your vocal coach about vocal fry, which can help keep your vocal cords connected. Be careful using that technique unsupervised, as it can do serious and permanent damage to your voice if you misuse it.
