YouTube could share time-stamped links on the desktop for a while now. Now, Android users are getting this option, too. There are a few steps you need to do to share specific chapters in videos. You have to make sure the video you want to share has video chapters, to begin with. When they do, the chapter title is visible on the playback progress bar. And when you tap that, you'll see the different chapters with timecodes and a share button to the right that will redirect you to Android's share sheet.
It isn't clear if this is a server-side update or not, but we've checked our OnePlus 9 and found version 16.25.37 already has it. According to 9to5Google, those with YouTube for Android v.16.20.35 and newer seem to have the feature.