Why do some strong players play 5... Be4 in Caro Kann, Tal Variation? [FEN &quot;&quot;]
1. e4 c6 2. d4 d5 3. e5 Bf5 4. h4 { B12 Caro-Kann Defense: Advance Variation, Tal Variation } h6 5. g4 Be4 6. f3 Bh7  7. e6 Nf6

What is the point of the intermediate move 5...Be4 before retreating by ...Bh7? It was played by very strong players, including Ding Liren (against MVL) and Hikaru Nakamura (against Mikhail Antipov).
If the point is to provoke f3, it seems to me that White is not unhappy to play f3 and control e4, as Black might play 6... Nf6 next, which is indeed a good move in these positons.
If the point is to disallow Nf3 in positions when White pushes e6 and Black takes with exf, it does not achieve that, as Black wasted one tempo on the bishop retreat Bf5-e4-h7 and White can also waste a tempo by playing f2-f3-f4 and then Nf3.
It does weaken g3, which Black could try to exploit with 7...Qd6, but after exf+ Kxf7 White can once again push f4 without feeling bad about wasting a tempo.
White probably intends to play e6 anyway, to launch an attack against the light squares. Whether Black takes this Pawn or allows exf7, White will want to play Nf3-e5 as part of his followup, and if f3 has been provoked, he will need to play f3-f4, losing another tempo and obstructing his dark Bishop.