A short outreach routine that puts you in lists already ranking for your term.
The best-tools lists ranking for your category already exist. Getting added to one is an email, not a campaign.
Search your category term and note every list on the first two pages. Those are the only ones worth contacting.
One specific reason your tool belongs in that list, referencing what the list is actually about. Two sentences.
A free lifetime account for review is normal and disclosed. Paying for a slot in an editorial list is a different thing and it eventually surfaces.
Then leave it. Authors update these lists on their own schedule, usually quarterly.