pi-base
Space Suggestion: Realcompactification of Rudin's Dowker space
Space Suggestion
Let $X' = \{f\in \prod_n (\omega_n+1) :\forall_n \text{cf}(f(n)) > \omega_0\}$
Rationale
This is realcompactification of Rudin's Dowker space $X$, defined in the original article by Rudin, and proven to be ultraparacompact.
Relationship to other spaces and properties
I'm not sure what any new searches it satisfies if anything... that's why there might be no real reason to add it, other for being interesting as the realcompactification of Rudin's Dowker space. If you know any, let me know.
Slightly ad hoc, but I suppose it satisfies this search: https://topology.pi-base.org/spaces?q=P-space+%2B+ultraparacompact%2B+Tychonoff+%2B+not+T_5
Ultraparacompact P-space which is $T_1$ needs to be $T_4$, and Fortissimo space on reals is the only non-discrete example. Its $T_5$ but not $T_6$. Ultraparacompact P-space which is $T_6$ needs to be discrete. And ultraparacompact P-spaces which are not $T_1$ exist as well. So this would fill the gap in terms of separation axioms when it comes to ultraparacompact P-spaces.