I have been making websites for many years now, and have always created a favicon.ico.
But over the years many other "standard" icons have appeared, for mac, for windows, for android, for iphone, etc, etc, etc.
Personally I have always ignored them ... but maybe it is appropriate to put at least some?
To have them or not, will it affect the SEO and search engine indexing of a website?
From a technical point of view, a single SVG icon would be a good thing. I you want you can target each platform individually:
Android Chrome - https://developers.google.com/web/fundamentals/web-app-manifest/
Edge and IE 12 - https://learn.microsoft.com/en-us/previous-versions/windows/internet-explorer/ie-developer/platform-apis/dn320426(v=vs.85)
Desktop browsers -
<link rel="icon" type="image/png" sizes="32x32" href="/icons/favicon-32x32.png">
<link rel="icon" type="image/png" sizes="16x16" href="/icons/favicon-16x16.png">
<link rel="shortcut icon" href="/icons/favicon.ico">