@Alexs welcome to the Atlassian developer community.
For Bitbucket, you can use OAuth 2 to create a simple API client, without building an Atlassian Connect App. In case you aren’t familiar with all the OAuth 2 grant flows, the “Authorization code grant” would allow your client to “act as user”. However, there isn’t any way to add consumers automatically.
Connect Apps have “scope” that can be account (more or less workspace) or user level. And, to be clear, Apps can be added multiple times to multiple accounts or users. They are not “bound” to only 1 specific workspace. That’s probably the better option if you want to distribute what you are building because there is both listing in Bitbucket and in Marketplace.