From the Fairy (UA) race, Fey Passage:

You can squeeze through a space as narrow as 1 inch wide.

And the rules for squeezing in basic rules:

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.

Would this enable a Fairy PC to escape from manacles, ropes that are tied around them, etc?

In UA 2021: Folk of the Feywild, the description of the Fairy race's Fey Passage trait says:

You can squeeze through a space as narrow as 1 inch wide.

And the basic rules provide the following rules for squeezing into a smaller space:

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.

Would the Fey Presence trait enable a UA Fairy character to escape from manacles, ropes that are tied around them, etc.?

From the Fairy (UA) race..

You can squeeze through a space as narrow as 1 inch wide.

And the rules for squeezing in basic rules..

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.

Would this enable a Fairy PC to escape from manacles, ropes that are tied around them, etc?

From the Fairy (UA) race, Fey Passage:

You can squeeze through a space as narrow as 1 inch wide.

And the rules for squeezing in basic rules:

A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it's in the smaller space.

Would this enable a Fairy PC to escape from manacles, ropes that are tied around them, etc?