project has 25 distinct synonyms spread across 9 of its 14 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
communicate vividly
“He projected his feelings”
transfer (ideas or principles) from one domain into another
project on a screen
“The images are projected onto the screen”
cause to be heard
“His voice projects well”
any piece of work that is undertaken or attempted
“he prepared for great undertakings”
Synonyms, antonyms and the broader and narrower relations for project come from Princeton University’s WordNet. Full sources and licences.