Simply creating a request object would not count as another billable Worker Request, nor as a subrequest.
actually fetch()ing within your Worker counts against your Subrequest limit (Limits | Cloudflare Workers docs). Which is 50 on free per request and 1,000 on the Standards Workers Paid plan. Subrequests don’t cause another billable Request or anything like that (unless you fetched another Worker of your own), there is merely limits on the amount of subrequests you can do per incoming request depending on your plan.