I'm not sure we know what to expect out of the budget for 2022, or what kind of signings will occur once the CBA is finalized. I don't know what kind of budget the Tigers had to being with. I would prioritize another SP ahead of an OF, I think there is still a need in the rotation.
Cots has the Tigers at $116.3M for 2022 (and they also use the correct old English D), and bbref has them at $115.1M.
I question Meyers' defense, but I think his bat would be helpful. Grossman had a career type season, Baddoo had a nice rookie season, Hill has a great glove when healthy, and there are high hopes for Greene. But its not a stacked OF by any means.
I understand the hesitation at first, but this isn't going to be a typical offseason. If there is a short window in between the CBA and spring training, I think there could be a lot of short term deals signed, and possibly some bargains that the Tigers could take advantage of. That's probably the best route to adding another OF (if needed). But I wouldn't shut out San Diego's desire to move Myers just yet. They might feel pressure to move him, and if its a short window of opportunity to do so, the level of prospect attached to Meyers might need to be improved. And regardless of who is on the major league team now, there's always room for more prospects in the minor leagues.