As per bug T72625: Migrate Tools access request process to Phabricator, if possible, moving the process to Phabricator seems like a good idea. This would probably not need any extension to display extra links or such as AFAIK setting up Labs projects is more interactive anyhow.
Why do you need an extension? Would a link to create a task with pre-filled description work as well? See T91538: Make new tasks within a specific project use a template in description field