synchronize_terminal_measurements() misorders measurements with the same key #6329

Description of the issue

(not 100% sure this isn't intended behavior)

when two measurements have the same key, reordering them results in a logically different circuit. Transformers like align_left() and align_right() correctly account for this by preventing the reordering of measurements with the same key, but synchronize_terminal_measurements() does not (see below)

How to reproduce the issue

circuit = cirq.Circuit(
    cirq.X(cirq.q(1)),
    cirq.measure(cirq.q(0), key="key1"),
    cirq.measure(cirq.q(1), key="key1"),
    cirq.measure(cirq.q(1), key="key2"),
)

print(circuit)
print(cirq.align_right(circuit))  # no change, as it would require reordering the two measurements with `key="key1"`
print(cirq.synchronize_terminal_measurements(circuit))

prints:

0: ───M('key1')───────────────────────────

1: ───X───────────M('key1')───M('key2')───

0: ───M('key1')───────────────────────────

1: ───X───────────M('key1')───M('key2')───

0: ───────────────────M('key1')───

1: ───X───M('key1')───M('key2')───

where the final circuit is not logically equivalent (the expected measurement outcome for "key1" is flipped)

Cirq version

1.3.0.dev20230830191034