The correct phrase is "eat healthily." "Healthily" is an adverb that describes the manner in which you eat, indicating that you are consuming food in a healthy manner. So, the correct usage would be to say "eat healthily" to emphasize the action of consuming food in a healthy way.

So the whole world, even google is wrong, though you are correct, i doubt it.....

Dude... https://www.google.com/search?q=it+is+important+to+eat+healthy+or+healthily++when+pregnant&sca_esv=2f37674a3ad0ce97&sca_upv=1&rlz=1C1GCEA_enSE942SE942&sxsrf=ACQVn09mwJ43_G34K_OvEqpd_zd8sZdf4A%3A1711996640120&ei=4P4KZoDrBovKwPAPx_GRkAs&udm=&ved=0ahUKEwiA29y81KGFAxULJRAIHcd4BLIQ4dUDCBA&uact=5&oq=it+is+important+to+eat+healthy+or+healthily++when+pregnant&gs_lp=Egxnd3Mtd2l6LXNlcnAiOml0IGlzIGltcG9ydGFudCB0byBlYXQgaGVhbHRoeSBvciBoZWFsdGhpbHkgIHdoZW4gcHJlZ25hbnQyCBAAGIAEGKIEMggQABiABBiiBDIIEAAYgAQYogQyCBAAGIAEGKIESKchUKgDWIYecAF4AZABAJgBqgSgAdEcqgELMC44LjEuMy4wLjK4AQPIAQD4AQGYAgegAswHwgIKEAAYRxjWBBiwA8ICBBAjGCfCAgYQABgIGB7CAgYQIRgKGAqYAwCIBgGQBgiSBwMxLjagB7w5&sclient=gws-wiz-serp It is important to eat healthy during pregnancy.... Just so you know!

hahahahahahah. No of course not!