Non tendering him seems pretty dumb. Yes 7 mil for a reliever is a decent chunk in a year they aren't "going for it", but its also doesn't prevent them from signing anyone else and he could be a great trade chip if they don't intend to resign him in FA.
If he needs surgery after an off season of rest sure don't pay him to be hurt, but barring that its an easy tender in my mind.
Rogers is a no-doubter to sign if his finger has recovered, and based on the timeline... it really should be provided he doesn't need surgery after all. Since surgery was an option, but not an absolute requirement, I'm taking a wild guess that Rogers was dealing with a pretty serious Grade III pulley strain issue.
https://theclimbingdoctor.com/pulley-injuries-explained-part-2/#:~:text=6-8 weeks is the,ROM exercises after immobilization phase.
Grade III – Complete A2 or A3 rupture (Most common pulley injury – A2)
3 months are recommended for a return to FULL climbing activities due to the biomechanical implications of an A2/A3 pulley rupture. Immobilization for 10-14 days is necessary to protect the pulley and after the immobilization/splinting process, you will use a thermoplastic pulley ring provided by a doctor instead of tape (more on the ring later). Passive ROM exercises following immobilization. Functional exercises will begin at the full 4 week mark, and EASY climbing will commence after a 6-8 week period from injury onset. At 3 months you can begin full climbing activities, and you’ll wear the pulley ring (or tape) for roughly 6 months after climbing begins again.
In the linked website from The Climbing Doctor, it says full climbing can resume in about 3 months with taping... that was a month ago for Taylor Rogers, and full and complete recovery around 6 months. I haven't heard a thing about Rogers throwing recently. Just that he was scheduled to see a specialist in September, which should have been about where he could resume full normal physical activities.
Obviously, pitching is different than climbing, but the stresses on the finger from climbing would be greater than that of a typical pitcher throwing, I'd assume. Why? Because the finger strain seems to be relatively common for climbers and very rare for pitchers. Just a guess though.
If Rogers hasn't recovered from the strain, it's a bad sign he'll need to go the surgical route and now we're starting to get to the point where his 2022 is in clear danger. It's worth noting, articles on the surgery indicate it's not always fully successful in that pain can persist and range of motion can be impacted, requiring potentially another surgery.
If Rogers is going to need surgery, the Twins' situation becomes a lot murkier and I'd pass on signing Rogers.