As @Silver and @joethei explained, you need to enable “Core plugins” from Sync setting in your online Obsidian account settings. Then restart the Obsidian mobile app:
Took me ages to figure out how to then actually see starred notes: on mobile, tap on the “Files” icon itself (where it appears under the title of your remote vault name, x files, x folders). That will reveal additional Search, Tags, and Starred options. I wish this was explained anywhere in the Help section.