A message, it seemed, had been delivered, one that Carl E. Heastie, the Assembly speaker, who is in charge of seating assignments, later elaborated on.

“It’s a challenge when people don’t get elected on the Democratic line but then want to sit with the conference,” Mr. Heastie said on Wednesday, noting that when Mr. Bohen won his April 24 special election, a local Republican Party chairman appeared on stage with him. “I think the message that we want to send is that you should run as a Democrat and sit as a Democrat.”

“He tells me he’s a true Democrat,” he added. “But he’ll have to prove that.”

Such statements are not made in a vacuum in the Capitol. In the State Senate, the Republicans control the chamber by a single vote: That’s the one possessed by a Democrat, Simcha Felder, who nonetheless sits and caucuses with Republicans, giving them a crucial 32nd vote in a 63-seat chamber. (Mr. Felder, who says he is loyal to no party, also ran as a Republican, unopposed, in his last re-election campaign, in 2016.)

Mr. Heastie said his situation in the Assembly is entirely different, as Democrats hold an overwhelming numeric advantage, regardless of where Mr. Bohen sits or which party he votes with. But he also suggested that there were certain concerns among Democratic Assembly members about espionage inside their members-only meetings, in which he said “sensitive” issues were often discussed. “So there’s also a trust concern,” Mr. Heastie said.

Assemblyman Ray Walter, a Buffalo-area Republican, said he suspected that the Democrats would eventually welcome Mr. Bohen back into the fold. “They’re trying to prove a point,” he said, adding that Mr. Bohen wasn’t really welcome in the G.O.P. either, since he supports Mr. Heastie. “If he changes his mind, we’d certainly consider it.”