Zeisler tries hard--you can tell he wanted to make an impression. I think he would've made more of one if he'd gotten up the gumption to jettison the tacked-on "it was all a dream" ending.
As Mark noted, Warren William dialed up a variant of his unctuous 30s persona as the policeman.
There has been a litany of films made all around the world from Dostoevsky's novel, but unless screening room cinema can be resuscitated in the world after COVID we're not likely to see a series featuring them. In addition to FEAR, we have the following:
1913 Russian silent version
1917 USA silent version
1923 German silent version directed by Robert Wiene
1935 USA version directed by Josef von Sternberg
1935 French version directed by Pierre Chenal with Harry Baur & Pierre Blanchar
1945 Swedish version directed by Hampe Faustman (who also played Raskolnikof)
1951 Mexican version directed by Fernando de Fuentes with Roberto Cañedo
(this one is also very noir-inflected; de Fuentes made many overheated melodramas in the 40s featuring Maria Felix as a femme fatale)
1956 French version directed by Georges Lampin with an all-star cast of French noir regulars (Gabin, Hossein, Vlady, Blier, Gérard Blain)
1957 Egyptian version
1959 USA version entitled CRIME & PUNISHMENT U.S.A. directed by Denis Sanders with George Hamilton (!), Mary Murphy, Frank Silvera...this is the one to pair up with FEAR
1970 Russian version 3:41 long, dark, grueling (shot in black & white)
1983 Finnish version directed by Aki Kaurismaki highly-regarded modern update
2000 CRIME AND PUNISHMENT IN SUBURBIA "teenage" version, better than one could possibly expect...
2015 Australian version
Of course, there are also films loosely based on Dostoevsky's novel that are not called CRIME & PUNISHMENT. The IMDB review Cineanalyst has compiled a list of 24 of them that can be read here...some of the other films included on the list are Bresson's PICKPOCKET, Woody Allen's CRIMES & MISDEMEANORS and MATCH POINT and several more obscure titles...it's worth a read.