My first reaction is, "Gimme Yates or Yimi, if the latter shows himself healthy."
Jansen will be too expensive, both in dollars and prospects.
The Reds saw themselves as competitive before the season and aren't that far out of it. They don't give up someone like Cruz, with control through 2028, without asking a high price.
When I'm In contention, if I'm going to give up something, I want someone with a track record, so not Nardi and Mears.
Yates and Yimi both have track records. They are in the last year of (manageable) contracts, which lessens the price. Without going too far into the weeds, I wonder if the Romo deal is comparable to what it would take for Yimi. Yates probably costs a bit more,
All in all, it seems like the Twins have improved their bullpen most years by regular churning guys, giving guys a decent amount of rope to prove or disprove, moving on to the next one when someone has disproved. In building an octet, it seems like we've got...
In: Duran, Jax.
Assumed in when healthy: Stewart.
Close to cementing their in-ness: Alcala, Staumont, and I'll include Okert.
Assuming health for Stewart and consistency for the next three, we're at six.
Undecided, pitching okay, but not yet in: Sands.
Still on their long leash, but trending downward: Funderburk, Thielbar.
Next guys to get a shot, on the 40-man (including 60-day IL): Winder, Henriquez, Boushley, Topa, Weiss.
Next guys to get a shot (or second shot), after the 40-man guys have been sorted out: Wittgren, Brigham, Castillo, Jensen, Jackson, Bowman.
I may have missed someone, but those are the general categories. I didn't include any of the guys being used as starters.
As I walk through this exercise, I start to think that there are enough options already in the mix. Assuming Stewart's back by soon after the All-Star Break and pitches well, unless there are injuries within the "in" group, I'm not sure how much is needed. Stewart makes six. With today, Sands will have moved his ERA+ to just above 100. If he would pitch himself up the latter to the in list, you're down to needing to only fill one spot from the 13 guys in the last four bullets, many who have shown extended stints of success at some point.
With all that, I'm not sure that I give up much of any assets to get Yates or Yimi. I don't know that the marginal gain from one of them is worth it.