I'm not really familiar with this stuff, so I might be completely wrong but:

From the contant_time_eq docs:

// Not equal-sized, so won't take constant time.
assert!(!constant_time_eq(b"foo", b""));

We don't check the length anywhere so couldn't the attacker start by sending a one-byte token, and after they find a match send a two-byte token, etc...?

For context the comment from https://phab.comm.dev/D4199?id=13456#inline-26218:

[without using the constant_time_eq] This introduces a timing side channel attack where the attacker can extract information about how much of the request token is right by the amount of time the comparison takes

after they find a match

i'm not sure what you mean by this. an attacker could learn the length of the token, but that's not a big deal - there'd still be enough entropy for a proper token