Is there a positive verb "to not do anything about"?
For a positive verb meaning "to do something about," we have "address" or "handle."
For a negative verb meaning leave alone or not do anything about or not give attention to, we have "neglect." Also "disregard" is a more neutral word, but it specifically means to not pay attention to rather than to omit action concerning.
Is there a verb without negative connotation that means "to omit action or activity concerning; to not do anything about"?
Example sentence:
I am going to _____ this project, as I think the people running it are doing just fine on their own.
Edit: Since a couple people in the comments somehow think such a verb is intrinsically impossible—an interesting concept—I'll mention several other words that are similar in many ways and do not have any inherent negative connotation, at least demonstrating that it's not fundamentally impossible to have a word with the meaning I've described above, even if there isn't a well known word that does:
Words/idioms with similar meanings and without negative connotations include: abstain, refrain, leave alone, let be, hold off (on something), tolerate, live with.
Perhaps 'abeyance' is what you need. eg 'The project was put in abeyance' meaning it was suspended or held over without necessarily meaning for any negative reason. You could also say something had its priority reduced, or it was reprioritised, but this is a little negative.
The positive alternative to the concept of neglecting or ignoring something is to set it free or to release it. It has 'graduated' beyond the need for your involvement. However, release already has a different definition in the jargon of project management, and set free is perhaps overenthusiastic in the corporate space.
Consider cut loose:
cut loose 1 : to free from control or restraint cut us loose from the contract - M-W
Your example sentence would then be:
- I am going to cut this project loose as I think the people running it are doing just fine on their own.
If you don't mind the verb referring to yourself, you could retire:
- I am going to retire from this project, as I think the people running it are doing just fine on their own.
retire transitive verb 1c : to withdraw from usual use or service - M-W