Maybe I’m misreading this from wikipedia , however it seems that the newspapers at the time had the full opinions and not just the paragraph below:
The court’s opinion was extensively covered by period newspapers as no official court reporter was yet published in 1791, and the seriatim opinions were republished in the newspapers. Each of the five justices issued a seriatim opinion regarding the writ of error, and the justices unsuccessfully looked to common law precedent from state courts and pre-Revolution English case law including Coke and Blackstone’s treatises. Several of the justices expressed their reservations about the federal statute and suggested alternatives for filing within the ten-day statutory period, but nevertheless each justice refused to expand the meaning of the statute believing that only Congress had the power to do so.[4] In summation the Dallas reporter quoted John Jay and summed up the case holding as follows:On the first day of the term, Bradford presented to the court, a writ, purporting to be a writ of error, issued out of the office of the clerk of the circuit court for Rhode Island district, directed to that court, and commanding a return of the judgment and proceedings rendered by them in this cause: And thereupon he moved for a rule, that the defendant rejoin to the errors assigned in this cause. Barnes, one of the defendants, (a counsellor of the court) objected to the validity of the writ, that it had issued out of the wrong office: and, after argument, THE COURT were unanimously of opinion, That writs of error to remove causes to this court from inferior courts, can regularly issue only from the clerk’s office of the court. Motion refused.[6]
So is there more in a publication/online that could be found?
Prior to the Marshall Court, it was rare for the Supreme Court to issue a majority opinion. Rather, they would issue an Order, as above, with the individual justices writing separate opinions (the seriatim mentioned in the cite means this) explaining the reasoning behind their judgment.
So what you see is what you get, as far as ruling from the court as a whole is concerned. You can presumably read the seriatim opinions of the justices at the Dallas cite )the first few court reporters published their own volumes of reports, which are referenced by their names).