what's the point of 5...Be7 in the Ruy Lopez ?

After 7.d3 I would try 7...Nc5

Maybe I'm way off but it seemed to me that Black's usually not too concerned with winning e4 but more castling and protecting e5.

In the Ruy Open, black takes e4 but White seems to get e5. I'm not sure that Black can ever get e4 clean unless White just blunders it away.

...Be7 allows quick castling and does offer dark square protection on the Kside. Where White often goes for pressure. In the Zaitsev, Black even drops the B back to f8 to help protect against any sac tricks on h6 and/or g7 allowing the f6N some options.

In the Archangel lines, it seems black often plays the DSB to c5, more aggressively pressuring White's King and f2. On the downside black's DSB doesn't help on the Kside and is often a target. Getting pushed back on the diagonal or traded away.

I've seen lines where Black goes for ...Bg7. Didn't Carlsen play one recently? But I've never really looked into it much.

In the "classical" line, it just goes there so you can castle. Oddly enough, it often repositions to f8-g7 afterwards.

In the Archangel Variation, Black plays Bishops to b7 & c5.

Sometimes it goes to c5 on move 3.

I think you may be mistaken.  I think what you've read is that after 5...Be7 6.Re1, White is threatening to win a pawn with 7.Bxc6 and 8.Nxe5.  This is finally a real threat because 6.Re1 has protected White's e4 pawn, so Black doesn't have the usual ...Qd4 antidote after Nxe5 -- it's no longer a double attack on both e5 and e4, because e4 is protected.