Yes, I have followed these studies for a while.
It is the butyric acid. Butyric acid has anti-bacterial, anti-inflammatory, anti-cancer, neuroprotective properties and cardio-protective properties (https://link.springer.com/article/10.1007/s00424-019-02322-y).
These effects seem to be mediated by epigenetic changes that as histone deacetylase inhibitor https://en.wikipedia.org/wiki/Histone_deacetylase, https://en.wikipedia.org/wiki/Butyric_acid
The production of butyric acid is not specific to Clostridium Butyricum, but also by * Clostridium kluyveri
These are bacteria that are that naturally occurring in your gut. They use fiber like resistant starch, pectin and other kinds of fiber to produce butryic acid.
It is true that butyric acid is one of the most hopefull compounds in the fight against dementia, other neurodegenerative diseases and colon cancer (especially FAP).
As PFS and PSSD also fall in the group of neurodegenerative diseases and as PFS also has vacular and cancer risks I understand why you are interested in the compound. Also there had been a study that showed that PFS patients have microbiome issues (probably the same for PSSD).
The field of microbiotic studies is relatively young. A and healthy (diverse) microbiome produces a sufficient butyric acid.
Now keep in mind if you ad single strains of microbes to your gut, this is like an invasion of billions of bacteria that your gut maybe is not prepared for. A healthy microbiome is balanced and consists of many different strains. I would say it is too early to say if probiotika really are safe and efficient. There had been also studies that people after antibiotics better recover their microbiome with prebiotics and not with probiotics.
Prebiotics are fiber rich foods. Like untreated wholefoods, berrries, whole grains, inulin-rich vegetables like onions, garlic, broccoli, chicory…
I am following the microbiome research and preventive medicine. IMO prebiotics are at least as effective, safer, and a lot cheaper.