From the horse's mouth:
Indeed, the only Frobenioids that are used in the IUTeich papers are the
(F1) tempered Frobenioids, i.e., a generalization developed in [EtTh], §3, §4,
§5, of the geometric example given in [FrdI], Example 6.1, to the case of
the tempered coverings that arise in the theory of the theta function;
(F2) Frobenioids associated to number fields as in [FrdI], Example 6.3 (cf.,
e.g., [IUTchIII], Example 3.6), together with the realifications associated
to (certain of) such Frobenioids;
(F3) certain special cases of the p-adic Frobenioids discussed in [FrdII], Example 1.1 (...) together with various related Frobenioids obtained by forming associated realifications or by forming the quotient...
(F4) copies of the archimedean Frobenioid discussed in [FrdII], Example 3.3,
(ii) (i.e., the Frobenioid denoted “C”).
Here, we note that (F3) and (F4) are inessential since a Frobenioid as in (F3)
essentially amounts to (i.e., may be replaced by) a suitable topological monoid with a continuous action by a topological group, while a Frobenioid as in (F4) essentially amounts to a copy of the topological monoid [that is the punctured closed unit disc of $\mathbb C$].
At any rate, from the point of view
of studying IUTeich,
(I1) in [FrdI], one may assume that all Frobenioids are model Frobenioids (cf.
[FrdI], Theorem 5.2, (ii)), which implies, in particular, that every object
of a Frobenioid is isotropic, and that every morphism of a Frobenioid is
(I2) one may in fact ignore [FrdII], §3, §4, §5.
It's worth looking at these slides by Weronika Czerniawska, especially the second set from page 15 on. On page 14 she says "almost all of Frobenioids appearing in IUT are model Frobenioids" and "Those which are not can be easily dealt with without notion of Frobenioid." She then goes on to detail exactly which ones are used.