AA/Beeston would only do value contracts. (Closest they came to "overpaying" was Russell Martin and he was worth every penny.)
The current front office has repeatedly shown a willingness to spend with the best of them for the right free agent. Sometimes the players agree to take the Jays money (Ryu, Springer, Gausman) and sometimes they don't (Ohtani, and surely some others we doon't even know about)