“There is no singular “they.””
There is. From dictionary.com:
nominative singular pronoun:
(used to refer to a generic or unspecified person previously mentioned, about to be mentioned, or present in the immediate context):
Whoever is of voting age, whether they are interested in politics or not, should vote.
A person may enlist only if they are over 18.
(used to refer to a specific or known person previously mentioned, about to be mentioned, or present in the immediate context):
The victim refused to testify at the trial because they feared for their life.
My best friend from high school is famous now—too bad we didn’t stay in touch after they moved to California.
(used to refer to a nonbinary or gender-nonconforming person previously mentioned, about to be mentioned, or present in the immediate context):
Quinn is waiting for summer vacation to adopt a puppy, so they will have more time to get their new family member properly settled.
Modern English dictionaries are not guides to usage or often even words even the New Oxford. After the Webster’s 2nd International the dictionary started entering everything that could be sourced to three speakers. Correct for modern dictionaries is whatever people use, in Boston or in Watts. They is third person plural. Period. If you want to give in to the leftist continuing restructuring and destruction of the language and thereby of thought processes- language being the tools of thought, then just go ahead and say whatever is handed down to you from a leftist academician.