Well, even in the past they were semi-public, meaning that they'd answer your question if you asked a priest or the bishop or their superior, etc. "Are you conditionally ordained?"
But they've never published who's who in any kind of formal place.
I'll share with you a story about early 1990s Winona (Bishop Williamson was still rector). There was a certain "Father"[?] Bibeau who just showed up there one day and was saying Mass at the main altar. We always kept a copy of Cor Unum around, a directory of SSPX priests, to see if it said they had been ordained SSPX. Well, this new "priest" wasn't in there. So some of us went around making inquiries. We eventually found out that Father Bibeau had in fact been conditionally ordained by Bishop Williamson in Our Lady's chapel (second floor). While it was private, the sacristan in charge reported that he was told to set up for a conditional ordination ... and then we found out who the target had been. Even back then, you had to make inquiries very discreetly, since the entire stink from "The Nine" was still fresh, having taken place merely 5-6 years prior to my arrival there. So if you were open about your "questions", you'd be suspected of being an SV-sympathizer if not an SV. So, my brother Steve had been in this group, except not at al SV, just had problems with the NO Orders, despite being decidedly R&R. Yet even he had to be very quiet about it, for these reasons. Steve was one of the main MCs at the seminary during his day, and he'd often hold the Missal during ceremonies, and there was one ordination in general where the bishops opened by banishing the "schismatici", and Steve, while holding the Missale, looked sideways to the other seminarians who knew his views, making a smirk, causing them all to crack up ... since the allegaion was that only "schismatics" questioned the NO Holy Orders, i.e. that was the current gaslighting at that time.
Eventually my brother Steve, after finishing 4 years and having had no issues, was shipped out to St. Mary's. Why? Well, he told a spiritual director at a retreat in Los Gatos (one summer during seminary) that he was concerned that his spiritual director was a Modernist. Despite spiritual direction being indirectly covered by the seal of Confession, this priest relayed / leaked this information back to the seminary staff ... at which time Steve was banished to St. Mary's to "consider" his vocation. Realizing he was being railroaded, he ended up leaving St. Mary's, leaving him dejected and extremely sad. That's to say nothing of the extreme scandal of a spiritual director leaking information to the seminary staff.
So, the identity of his spiritual director that Steve denounced as suspect of Modernism?
One Carlos Urrutigoity ... who ABSOLUTELY was a Modernist. 100%. I myself had denounced him as such to Fr. Bourmaud, God rest his soul, when on one occasion Bishop Williamson was out of town and he was acting rector. Urrutigoity was engaging in various liturgical experimentations that had been banned by the Council of Trent (troped Kyries) and also wanting to admit women into the choir. Fr. Bourmaud put an immediate stop to that, but it showed U's true colors. He's done and said many things that indicate he was a Modernist and no Traditional Catholic, just going Trad in order to get better cover for his predation. In fact, you KNOW you have something warped about your theological system when you can morally justify that kind of behavior.