Jira currently does not allow for the native use of OAuth with webhooks.

Currently, as described in a Community article on Jira automation Webrequest REST API

It is technically possible to set up OAuth using webhook triggers and actions, by manually performing the relevant OAuth steps (ie, fire off a web request to your OAuth provider's Authorization end point, with the redirect url pointing at another rule setup to listen on an incoming webhook, then from there hit the OAuth grant endpoint etc). This is very involved though, and is not really recommended, as it is complicated and somewhat brittle. Alternatively, you could manually generate an OAuth bearer token yourself, and configure rules to use that bearer token in your Authorization http header when making web requests. However, in that situation, users who have access to see the rule configuration would also be able to see the bearer token credentials.

These solutions are not ideal, and having Jira support OAuth on webhooks natively would be more useful.