Incremental is key here, 'modernization' sounds like a large and blurry goal. You need to get this under control as soon as possible, definitely don't "give it

Incremental is key here, 'modernization' sounds like a large and blurry goal. You need to get this under control as soon as possible, definitely don't "give it a couple of weeks and see if the team picks up pace". Start making lists, what has been done, what needs to be done, prioritize and start tracking that. Don't create big tasks that are measured in percentages (frombulating the gizmobob is 42% done). Make small tasks that are either done or not done (0 or 1). Small tasks meaning measurable in hours, not days, let the people who will do the work make the estimates. Don't worry, this is not micromanaging, this is properly managing a project, and yes, it will take some of your time keeping track of all of this. There is also the question whether should you be doing this or should the product owner be doing this? Obviously the PO is not doing this, and you have a leadership position, so I would not hesitate too much.