I know that in « peut-être » the t is pronounced and I was wondering whether the t is still pronounced between the peut and the être in sentences like « il peut être quelque chose » because it has a different meaning here and I was wondering whether the French distinguish aurally between the two.
As you say you always liaise when you pronounce the adverb peut-être [pœtɛtʁ].
When using the verb pouvoir followed by a vowel sound (not necessarily the letter "e") it is a case of non mandatory liaisons, although I suspect most people would liaise. I think I always do but I'm not surprised or shocked, if I hear [sapœɛtʁɛ̃tɛʁɛsɑ̃] or [ilpœavwaʁʁɛzɔ̃], so without a liaison.
In my variety of French the eu in peut-être is more often pronounced as a short [œ] if not dropped completely, whereas in peut être it is always pronounced [ø]. So when I read the phrase peut être, I tend to emphasize the [ø] and still liaise and pronounce the T.
In practice it's not a phrase that comes up all that often.