What do you think, as the place to start, in regards to your mention of overriding the Literal Expression grammar?
Currently, 👨‍🎨 I now have something like this in the PostgreSql.bnf and some other overridden types as well.
Where the LiteralValueMixin is a new type PostgreSqlLiteralValue

literal_value ::= ( {numeric_literal}
                  | {string_literal}
                  | {blob_literal}
                  | NULL
                  | CURRENT_TIME
                  | CURRENT_DATE
                  | CURRENT_TIMESTAMP
                  | interval_expression ) {
  mixin = "app.cash.sqldelight.dialects.postgresql.grammar.mixins.LiteralValueMixin"
  override = true
}

Also, the following existing time literals are not supported either as the LiteralValueMixin only allows them on assignment. The below results in Cannot use time literal in expression

SELECT CURRENT_TIME, CURRENT_DATE, CURRENT_TIMESTAMP

I may create a draft PR as I find out more - as this is quite a tricky one to sort out 🌵

I can also create an initial PR to add SqlTypes.INTERVAL to the sql-psi repo as is ANSI type (but not supported on Sqlite).