Falvey stated he wants Ober, Winder, Varland, SWR, Sands and Balazovic stretched out and starting. That means they're not options for the bullpen. I mean, they could be but that would mean they're not going to develop as a starter and they need to replace 3 starters this offseason.
Stashak and Legumina are gone.
Headrick (4.81 ERA), Laweryson (1.02 ERA), Funderburk (2.94 ERA), Bentley (3.79 ERA), Cabezas (3.13 ERA), Gross (4.03 ERA), Enlow (4.40 ERA), Sammons (5.76 ERA), Scherrf (5.27 ERA) - none of them have pitched above Double-A and most of them kinda sucked at Double-A. I'm not big on giving scholarships to minor leaguers who haven't proven themselves at AAA. Austin Schulfer (0.39 ERA in AA, 5.23 ERA in AAA) is a good example of why that's a bad idea.
So you're left with Danny Coulombe. If the Twins like him better than Hand, that's fine (I don't). Oliver Ortega is a guy they grabbed and waived as a AAA stash. They still need to go get one (or more) of the other veteran relievers on the market because their bullpen is 3 pitchers deep off the 26 player roster.
And I think you're actually confused about the process. They have 2 spots open on the 40 man roster once they put Paddack and Canterino on the 60 day injured list. They have a unique opportunity now because there are decent veteran pitchers available and they have an open roster spot. This opportunity goes away before the season begins.
If they add one of those Double-A guys they can option him if he sucks, but then then he's on the 40 man and they can't remove him without allowing the league to grab a young pitcher for free. If they remove Enlow again he can elect free agency. You don't add pitchers with a future to the 40 man roster until they're ready to contribute or you're forced to because they are at risk of being taken in the Rule 5 draft. It's better to cycle through veterans.