FWIW, the Cowboys have often been near the bottom in actual cash spending. For example, from 2016-2020, they were dead last in actual cash paid to players. That likely changed a bit with the extension to Dak in 2021.
So the fact they are low on this measure isn't all that shocking. There is a variety of reasons why the Cowboys seemingly are always up against the cap but not high in actual cash spent. One is that the Cowboys aren't as quick as other teams to dump players. Cowboys hold onto guys longer whereas other teams will cut dead weight sooner and then throw cash at FA to fill the hole.
Here's an example:
Dallas signs Player A, a DE: 3 years, $50MM, $20MM signing bonus.
Year 1 - $30MM cash ($20MM signing bonus + 10MM base)
Year 2 - $10MM cash
Year 3 - $10MM cash
$50MM in cash over three years.
Tampa signs Player B, a DE: 3 years, $50MM, $20MM signing bonus.
Year 1 - $30MM cash ($20MM signing bonus + $10MM base)
Year 2 - $10MM cash
Player is cut after Year 2. They sign another DE in FA for 3 years, $60MM with a $20MM signing bonus
Year 3 - $32MM cash ($20MM signing bonus + $12MM base)
Total cash spent by Tampa in those three years: $72MM