As I understood so far with the help of Urban Dictionary, it means to act in an overly embarrassing way. Am I right? The whole sentence is:
Every week, we think Succession has hit peak cringe.
peak cringe has yet to reach a registered idiomatic phrase in major AmE abd BrE dictionaries.
So it a matter of using the figurative definition of a verb and the definition of a noun:
peak a noun. vocabulary.com
the most extreme possible amount or value
cringe. OED a verb
b. figurative. To experience an involuntary inward shiver of
embarrassment, awkwardness, disgust, etc.; to wince or shrink
inwardly; (hence) to feel extremely embarrassed or uncomfortable.
Every week, we think the tv hit Succession has achieved maximum awkwardness and disgust [cringing is at a maximum at this point in time] in its viewers. It will likely continue to reach new levels of such as the season progresses.