Feasibility of Grand Tack Hypothesis Something I've been wondering lately is how much the grand tack hypothesis stands up to present scrutiny. While the grand tack proposes that Jupiter and Saturn were caught in a 3:2 mean-motion resonance which results in migration outwards to roughly close to their present distances, simulations of dynamics of planetary migration seem to indicate that a 1:2 MMR is much more likely to occur, which most likely does not result in migration outwards.
Also, a much more recent hypothesis suggests that Jupiter formed much further out than the present location and then migrated in over a period of ~700,000 years, which would explain the distribution of Trojans in Jupiter's orbit. The starting scenario of this hypothesis is completely different from the grand tack which states that Jupiter formed around 3.5 AU distance. It also says absolutely nothing about Jupiter and Saturn migrating further inwards and then back out due to resonance.
Can the grand tack hypothesis be reconciled in any way from these newer studies?
What you have to keep in mind is that the Grand Tack was devised as a mechanism to generate a truncated planetesimal disc between 0.4 and ~2 AU during the protoplanetary disc phase, in order to explain the small masses of Mars and Mercury (Walsh et al., 2011).
The smallness of Mars and Mercury might be explained differently by pebble accretion (Lambrechts et al., 2019), which wasn't fully worked out yet during that time.
A direct test of whether Jupiter/Saturn indeed migrated during their growth phases, is their Trojan number asymmetry, which is the basis of the paper by Pirani et al., which you quoted. They find that the Trojan-to-Greek numbers should be equal only in the case of in-situ formation, but they are not.
The observed asymmetry is consistent with migration inwards during Jupiter's growth. However, from their work, no clear statements can be made on

where Jupiter's core formed;
how fast the inward migration proceeded; or
whether there was a later outward migration.

Furthermore, the migration rates required for the Grand Tack to operate might be wrong. Recent work coming from people working on migration rates (McNally et al., 2019, Lega et al., 2020) seem to indicate that migration in low-viscosity discs works very differently than what was envisioned in earlier decades. Outwards migration, or stopping, is then easier for giant planets.
Summarizing, many of the puzzle pieces on why the Grand Tack was envisioned and how it worked are currently under active investigation. This is not an issue I expect to be solved soon, as certainty into any of those models would additionally require Trojan asymmetry numbers for Neptune and Uranus, and those are very challenging.