I figured it out.

@just King, Thanks for the Update, will the new custom field be rolled out in a phased approach? or, is there a specific setting that requires activation? Currently, I can only see the External Assets Custom field.

Hello!

I'm happy to announce that Assets custom fields are now available to be used in Team Managed Projects. 

All the best!

Justin King
Product Manager, Jira Service Management

@Justin King, we really need this feature but unfortunately, we are still using team-managed projects. We are considering create a company-managed project for this purpose, but it will require a lot of work. Even though the company-managed projects are generally more inclusive, it would be great to have this feature in the team-manages ones. Thus, would you be able to give more thorough update details, like when it could be implemented?

Insight object fields must be multi-selectable. This is very important, I'm having trouble with team-managed projects because they don't implement the multiple selection dropdown.

Hello! I have an update on this feature request. Until now this feature was not being considered. However, it is now something we hope to make available and work is in progress toward this. 

with a new ticket assignee does this mean we are considering this again?!
@Justin King ??

We do not agree with that decision since this feature (Team-managed/insight) existed with insight plug-in. 
Atlassian have forced us to go to JSM Premium to work with Insight and now we don´t have this feature at Team-managed.

I agree with @Sven - it's a complete mess!

When Atlassian announced and released next-gen projects it was a big step forward. Even the name itself was a promise that this kind of project type would be a future. Now next-gen isn't next-gen any more and Atlassian's says that old/classic/company-managed projects are their "strategic focus". 

They left customers in the lurch. What are team managed projects for?

To me, this decision is unclear. Now where early access to team-managed "service management" projects has been released, I thought they would be the project type of the future. We wanted to upgrade "service management" to premium just because of Insight, but I'm not willing to switch back from team-managed to company-managed just for asset management. Company-managed projects cause so much more administration effort.

BTW: You should update your documentation which indicates, that Insight is available for team-managed projects.