Can one be found guilty for defamation if they bring a completely
baseless trial against an individual/entity(without any public
statements or the like, just the trial itself), as trials are more or
less public events?
No. Someone can't sue for defamation for something said in a trial. There is an absolute immunity from defamation liability for anything said in a court proceeding. (Strictly speaking "found guilty" would apply only in criminal defamation cases which are vanishingly rare in the U.S., while "held liable" would be the proper terminology in a lawsuit for civil damages which is how almost all U.S. defamation cases are litigated.)
Would this differ for public vs private figures in practice?
The Restatement of Torts is a document prepared by distinguished law professors and a committee of leading experts on tort law, and approved by the American Bar Association, which sets forth majority positions on principles of the common law in a codified form, that are widely used as references for that purpose by state courts and adopted as law in circumstances where a state court has no clear case law on point. The Restatement of Torts sets forth a variety of absolute immunities from defamation liability (a common law tort) that are almost universally honored by state courts.
Both parties to litigation and witnesses have absolute immunity from defamation liability for statements made in connection with a judicial proceeding.
A party to a private litigation or a private prosecutor or defendant
in a criminal prosecution is absolutely privileged to publish
defamatory matter concerning another in communications preliminary to
a proposed judicial proceeding, or in the institution of or during the
course and as a part of, a judicial proceeding in which he
participates, if the matter has some relation to the proceeding.
Restatement (Second) of Torts § 587 (1977)
A witness is absolutely privileged to publish defamatory matter
concerning another in communications preliminary to a proposed
judicial proceeding or as a part of a judicial proceeding in which he
is testifying, if it has some relation to the proceeding.
Restatement (Second) of Torts § 588 (1977).
There are also similar absolute privileges from defamation liability for judicial officers (Restatement (Second) of Torts § 585), attorneys' at law for a party (Restatement (Second) of Torts § 586), and jurors (Restatement (Second) of Torts § 589).
The absolute privilege from defamation liability for attorneys for a party in connection with court proceedings has been described as follows:
Restatement (Second) of Torts § 586 (1977), adopted in Colorado in
Renner v. Chilton, 142 Colo. 454, 351 P.2d 277 (1960) states:
“An attorney at law is absolutely privileged to publish defamatory
matter concerning another in communications preliminary to a proposed
judicial proceeding, or in the institution of, or during the course
and as a part of, a judicial proceeding in which he participates as
counsel, if it has some relation to the proceeding.”
Club Valencia Homeowners Ass'n, Inc. v. Valencia Associates, 712 P.2d 1024, 1027 (Colo. App. 1985)
There is also a widely recognized (and arguably constitutionally required) qualified immunity from defamation liability for people making an accurate report of what was said in court that would otherwise be defamatory, so long as it is indeed a substantially accurate account:
[U]nder the common law doctrine of fair report, reports of in-court
proceedings containing defamatory material are privileged if they are
fair and substantially correct, or are substantially accurate accounts
of what took place. See Rosenberg v. Helinski, 328 Md. 664, 616 A.2d
866 (1992); Cianci v. New Times Publishing Co., 639 F.2d 54 (2d
Cir.1980) (recognizing common law privilege of fair report of public
court trials as far back as 1796).
Tonnessen v. Denver Pub. Co., 5 P.3d 959, 964 (Colo. App. 2000).
There are myriad cases upholding these privileges, which have been widely recognized even prior to the Revolutionary War in North American common law court cases adopting the English common law rules in place at the time.
Why Does Absolute Immunity Exist In These Circumstances?
There are several basic policy justifications for this form of immunity.
One is that is avoids the risk of collateral litigation arising from ordinary lawsuits and criminal prosecutions.
A second one that is closely related is that it eliminates the extraneous considerations that might discourage someone from being truthful at trial for fear of a defamation lawsuit which might be costly to defend even if the court participant prevailed.
A third one is that it creates an incentive to use the court system to resolve disputes over sensitive issues that could damage reputations, rather than in public relations fights in the media and other public forums that are less structured, or, for example, in duels (a pervasive problem in much of the U.S. until the late 19th century when they were effectively banned and American culture ceased to approve of them as valid or necessary to avenge one's honor).
Also, while defamation litigation is prohibited based upon statements made in court proceedings, there are, in principle, other means of punishing false statements made in court proceedings or other defamatory conduct in court proceedings. It is a crime, perjury, to make a false statement under oath in a court proceeding (although perjury is rarely prosecuted in practice relative to how frequently it occurs).
A judge can strike scandalous and unnecessary materials in court documents that would be defamatory, can order court documents placed under seal, can order that the public be barred from court proceedings in certain kinds of circumstances, can bar parties to court cases and their attorneys from disclosing otherwise secret matters in court cases, and can hold someone in contempt of court for improperly making defamatory statements public when they were ordered not to do so.
Finally, if a trier of fact does not believe a false statement made in a court proceeding, the judge or jury can rule against that person on the claim that the false statement supports, and a judge can say that the judge believed that the statement made was false.