They would not have infrastructure, but they would have knowledge
Debatable. Most people don't know the exact formula or process for gunpowder or combustion engines, just that they're possible. Even experts or people familiar with the trivia generally know it either in an advanced fashion (how steel is smelted nowadays, not how to do so yourself) or in purely hypothetical terms (how to create persuasive propaganda, not that they've ever done so in practice).
A military expert may know tactics that were developed later. (Martial)
A historian may know things long gone public. (Diplomacy)
An engineer would know how to build things better. (Stewardship)
A chemist would know how to make poisons. (Intrigue)
A doctor about could know about peniciline and would know how organs work. (Learning)
Advanced military tactics are generally valuable because they exploit advanced conditions, not because ancient peoples were too stupid to hold spears right. Knowing what tactics are to be used in the future doesn't help if you can't make those conditions true in the present.
An egghead from several centuries in the future trying to brag about contemporary events he read about in fragmentary sources sounds like the opposite of a diplomacy bonus. It sounds in fact like a comedy premise.
A modern engineer would know how to build things better with modern materials and equipment. He wouldn't necessary know anything about working cut stone or assembling a wood crane from scratch. For that matter, modern designs tend to be overengineered for safety but intended to operate for only a few decades. Medieval peoples might not consider those useful qualities.
I mean yeah, there's probably a few gems in there. Usually creating a poison isn't really the hard part of murder, though.
He might know
about Penicillin. That doesn't mean he'd be able to refine any. He would indeed know how organs work, at least broadly, but again- way, waaaaay easier to say "kidneys filter the blood" than perform useful diagnoses and surgery and medicine with medieval tools.
Sure, the lack of infrastructure would hurt most of these people, but they still could perform better than people from the past. Some things do not require much infrastructure.
About credentials, those are their work. They would have to get someone to try them and prove that they are that good.
Quick acid test for this- drop a guy from now into the 1920s. Would you expect him to be a better or worse 1920s mechanic, politician, lawyer, bartender, etc etc than people who were familiar with the time period? I see no reason they'd "perform better than people from the past" for most of these.