I don't know entirely out of escort missions, but I know there's one made entirelly of unskippable cutscenes. Classics like Dragon's Lair, Space Ace, and even Rockman Adventure, since the cutscenes are pretty much the game itself. Even worse, the entire game are Quick Time Events.

Ico

Lemmings? Bioshock: Infinite?

Sega’s Flicky from 1984 is a game where the whole gameplay is to play as a bird collecting and guiding its babies to the exit while avoiding enemies.

A Plague Tale: Innocence is well-received game that's game-long escort mission

Mario & Wario (that SNES mouse game that was never released outside Japan) is technically all escort mission. Also the Mario & DK games (the ones with the mini-Marios.) Basically every Lemmings game and games of that type too, for that matter.

shadwen is a stealth game where you have to take alternative routes to clear the normal path for a girl to follow

Isn't RE4 almost entirely an escort mission?

A game that's entirely escort missions?

..."Rocko's Modern Life: Spunky's Dangerous Day". Maybe "Yoshi's island" too depending on what you count as an escort mission