I want to be able to find specific keywords in domain names across the internet. Search ahrefs using a specific word to bring up all the domain names (not urls but actual live website domain names) that include that keyword.

Then you can filter with DR and traffic to get a highly relevant list of domains on the internet that have your specific keyword in it - then outreach to those sites to get a link to your site. Then repeat with all your target keywords to find more domains with your keywords in it. The links you get will be highly relevant and filtered for DA and traffic and whatever else you want to filter for.