Basically, yeah, but with the difference that these sysadmins are generalizing and abstracting the patterns they've learned over years.
I personally think of "devops" not quite so much as being about "dev" and "ops" collaborating (though that is a noble and worthwhile goal) as about having "developer-operators", people who know how to do operations effectively and who can turn that knowledge into automated, generalized software systems.
The abstract modules and tools can live in their own repositories (or folders, in a monorepo), and your devoperators can work closely with the product teams to use them (and abstract specific changes to meet projects' individual needs to be more generally applicable).
I personally think of "devops" not quite so much as being about "dev" and "ops" collaborating (though that is a noble and worthwhile goal) as about having "developer-operators", people who know how to do operations effectively and who can turn that knowledge into automated, generalized software systems.
The abstract modules and tools can live in their own repositories (or folders, in a monorepo), and your devoperators can work closely with the product teams to use them (and abstract specific changes to meet projects' individual needs to be more generally applicable).