For new sites, Google insists that the website is mobile-friendly. I just wonder, because of this it may want you to provide higher resolution icons as well.
Favicon takes longer than the website to appear.
Google Favicon user agent
Google Favicon is the user agent for downloading favicons defined by websites. It is a low-volume crawler: it may visit the home page of your site occasionally based on signals gathered during indexing, or triggered by a user request. To request that the Google Favicon user agent crawl your page, you can request indexing of your site's home page. Updates can take a few days or longer to appear in search results.
From Define a favicon to show in search results
I would request indexing and if you still haven't had a result in another two weeks, then consider providing some more resolutions (especially 192x192 for Mobile). There are sites around that will generate all the necessary resolutions for you.
Just last week, Yandex complained about one of my sites, saying that they wanted an SVG favicon. So I would provide that too.
Bing
Sometimes things can just go wrong. I had the same issue with one of my sites, so I wrote to support. They fixed it.
We got a response from engineering team and i would like to inform you that the Favicon has been updated. It is showing in Bing search results.