I'm trying to find the proper way to collect bugs/issues in Jira's next-gen projects. Looks like this feature has been requested by many users.
How other PM's are dealing with bugs in this case?
You can do that with issue types. Read more here on set up issue types in next-gen projects. By default, next-gen software projects come with the bug standard issue type which is used...
... to track problems with software, such as user interface discrepancies, broken functionality, or other niggles experience by users.
To add bug issue types:
If you're going to have many bugs and it's unlikely to do them all in a given Sprint, you might want to enable backlog because that way you won't have them all in your team’s board. To enable or disable the backlog: