~1/5 of Apple's Services revenue comes from having google be the default search ($9-10B per year), so I wonder if this new search will coincide with them ramping up their own search ads business [https://9to5mac.com/2019/11/15/apple-ad-revenue/]
Could be that contract is up for renewal? Google seemed like it was going to stop paying Mozilla this year, then changed their mind. Threat of building a search engine competitor could just be part of contract negotiation (a BATNA).
Or they could just say they'll use Bing instead. That's cheaper, provides a better experience for their users than their own search engine, and is a stronger threat to Google if they want Google to increase payment by encouraging more ad dollars chasing big spenders to go to Bing.