Seagulling

Seagulling (verb)
/ˈsē-ˌgil-iŋ/
1. The art of orbiting someone you secretly (or not-so-secretly) want, without committing to actual interaction—just circling, watching, and occasionally swooping in to drop a cryptic comment.
2. Often performed by people who want to be noticed but still keep the upper hand… or their dignity.

“She’s been seagulling me all week—everywhere I turn, there she is, pretending to check her phone but clearly tracking my every move.”