Yes why not come during April. Ryan, Easy jet and BA start end of March from several UK hubs and as from Mid April so do our European visitors from Germany and Austria who enjoy the Springtime walks and wild flowers,
You will not go hungry or thirsty - remember we live here all year round. However it may be advisable to have a car or some form of transport - village tavernas close by are open all year round and a few places will open in resort if/when they see people arriving too. Greek Easter being the weekend of 25/04 this year will no doubt be well supported especially in Corfu Town.
Accommodation wise - again yes you will find something - you can email san stefanos travel via their website. I know various long stay guests who rent and start to arrive end March/Beg April. Just ensure you have some form of heating and bring clothes for this kind of holiday.
Owners in resort also open if they have requests so you can check this out too. My friends with a hotel in Arillas open always (Pre Covid) in April. so yes you can find accommodation.
April is a lovely time to visit and experience the island. We normally start BBQ-ing come April and as Easter is falling late here sure many will be doing so too......