A standard rate turn is 360 degrees in 2 minutes for all planes.
However the bank angle required to accomplish this depends on
airspeed.
The Standard Rate Turn is a concept created a long time ago to standardize
turns so that they are predictable for both piltos and controllers.
They allow a pilot to perform any course change or turn while flying in
clouds without a compass or a heading indicator.
For instance, to change heading by 30 degrees, the pilot executes a
10-second Standard-Rate-turn if it's a small airplane, or a 20-second turn
in a jet.
The Standard Rate Turn is the rate-of-turn used by the autopilots when it
executes turns.

This however, has nothing to do with the aircraft's ability to perform steep
turns (45 degrees and beyond), or even rolls if the pilot wanted to.

For most large jets the cruise airspeed standard rate turn
would exceed 30 (maybe 45) degrees of bank.
This is the reason the Standard Rate turn in a jet is 1.5 degrees per second
or 4 minutes for 360 degrees turns.
Just a quick note : Airliners execute turns of AT LEAST 30 degrees bank
every time, except when performing small course corrections while in cruise.

Therefore they are restricted to 25 degrees of bank.
Where did you get this from ? There is no such thing. Airliners execute 45
degree banks on every flight.
25 degrees of bank doesn't produce much of a heading change in a jet, test
it yourself in FS.

Now, this does not mean a 757 can't physically turn more steeply than
that, it just states how they are governed. I'm sure a 757 would have
no problem performing a 60 or greater degree bank angle, just as the
707 had no problem being rolled during its test flight.

Correct. They can and they do perform steep turns every day.
The 757 and the 707, as well as all other Boeings (except the 777) have
"conventional" controls, meaning, the control surfaces are directly
connected to the cockpit (they may be hydraulically assited), and therefore,
they can do whatever the pilot wants them to do.
The newer "Fly-By-Wire" airplanes like the A320 and the subsequent Airbuses
have certain limitations built into the software to prevent sudden maneuvers
and to protect the airplane from undesired things such as stalling, but even
these will allow steep turns.