The senators are not jurors in a legal trial. They are political actors charged with the task of inquiring into an officer’s alleged misconduct and taking whatever action might be necessary to secure the public interest (constrained by the constitutional limit of removal and disqualification from office—no beheadings allowed).
The senators have a duty to do impartial justice according to the Constitution in the impeachment trial of the president. That surely means, among other things, that they have a duty to vote to acquit if they believe that the president has not committed an impeachable offense under the Constitution. It means that they have a duty to conduct a trial that provides both sides an adequate opportunity to present their case. They have a duty to consider the evidence and the legal arguments that are relevant to determining whether the president has committed an impeachable offense. They have a duty to vote to convict if they believe that removal is constitutionally justified.
That does not mean that they have to wait until the formal start of a trial to start assessing whether an officer has committed impeachable offenses or limit their deliberations to the specific evidence and arguments that the House managers and the counsel for the president might present on the Senate floor. That does not mean that they have to sit for the impeachment trial with an open mind and no prejudgments on the merits of the case. That does not mean that they have to refrain from making public statements about an officer’s conduct.