The preceding text has "uniquely identifies the current thread of execution", so the first part "no other thread" is redundant anyway.

Is there any concern about whether past or future threads might reuse IDs? Did the original "no other thread" wording imply anyhing stronger than just "uniquely identifies"?

In practice, we can't prevent thread-id overflow anyway.

And it was and continues to be uncertain whether "uniquely identifies" and "no other thread" refers to the entire history of the program, or just to the current instant.