How do you get your business stakeholders more invested in your team’s agile workflows?

Show them you're listening, working with them and helping them solve problems or improve product they care about. Fundamentally, they won't be very invested in the workflow, it's the outcome.
We delivered basic agile training to our key stakeholders so they at least understood the approach, roles and language we were using. That helped buy the team time and space to get things moving. Some of them still struggle with some of the agile concepts but at least they're not investing time in trying to change our approach any more.
Communicate, engage and deliver and keep doing it.

As CEO of Buinsoft, I think that: When it comes to be more agile, the communication is the first priority. With the right and often communication with stakeholders, getting the feedback from each and at the end showing the value can be good way to do it. 

Here is a video of my teams back in 2016, we have continued this sort of investment, releases  to production multiple times a day, no known bugs in production for many months to year+ at a time, psychologically safe environments. https://www.youtube.com/watch?v=dVqUcNKVbYg 

I wrote an experience report on how we scaled our teams https://www.agilealliance.org/wp-content/uploads/2017/02/GrowingTheMob.pdf 

I heavily recommend using the diffusion of innovation theory to guide your growth. Look for early adopters and put them on a team together, protect the team and allow them to deliver independently in an agile way with good technical coaching. Doing so will allow you to track DORA metrics which can then be used to show the benefits which can then be used to convince leadership to expand investment in these practices. Once at the Early Majority you can accelerate adoption. 

Reach out if you have any questions. 

Engage stakeholders meaningfully through your agile workflows. By involving them in decision-making and providing transparent updates, you'll foster a sense of ownership and commitment. When they see the direct impact of their contributions on valuable outcomes, their continued engagement and vesting will be more likely.