Updates are automatic with checks every ~6 hours by default. You can manually trigger a check but it's unnecessary.
Read these 2 sections for more information on update channels and other configuration options>
https://grapheneos.org/releases#about-the-releases
https://grapheneos.org/usage#updates
Every production release goes through the Alpha channel, then the Beta channel and then reaches the Stable channel unless significant issues are found during public testing. The channels provide the same production releases.