Yeah signing Alonso would mean they're not exactly rebuilding. Though they could still look to lower immediate term payroll even while adding other pieces.Nightengale also reported there are rumors the Cardinals could pursue Pete Alonso to take over for Paul Goldschmidt. That doesn't sound like a team looking to clip coupons.
I would be calling about Gray. And I think they will move him. But if you find out they aren't interested then of course move to other options.
MLBTR also seems to expect a Cardinals selloff. Lots of Cards at the top of their recently released trade candidates article.