I think 'I wish I were dead' is correct here. It's the subjunctive mood - indicated by 'I wish . . . '. But it would be common to hear 'I wish I was dead' but it's wrong.

It's correct to use the subjunctive "were" in your sentence. Nowadays it's common for speakers, especially British English speakers, not to use the subjunctive. On the other hand, there are many American speakers (more than the entire population of the UK) who still use the subjunctive even in casual conversation, and the correct use of the subjunctive (both past and present tense) is expected for formal writing in American English.

fyi, 'grammarly' is not a word; it's a brand of software. GRAMMATICALLY is the word you're looking for.

"I wish I were dead" is grammatically correct. People do say "I wish I was (something)" but it's better to avoid saying or writing that.

I wish I were dead' is grammatically correct.