What data types LibreOffice not support

Example:
Cannot show the secondary axis in the line chart

Retag your question as this is a LibreOffice site: there is nothing like Excel here. The spreadsheet app is named calc. You tagged draw, i.e. the drawing component. Are you also experiencing problems with it? If your question is only about charts made with Calc, remove tag draw. Thanks.

“Data type” can be an arbitrary entity, so listing “all unsupported data types” is futile. Rather, I guess you can show which data types are supported.

AFAIK
For spreadsheet work, to handle by formulas

The fundamental data types handled are number and string. Numbers are further subdivided to be handled as Boolean, simple scalar, date/time, etc. This subdivision happens by explicit formatting, implicit formatting by interpretation of data entry format, or (for formulas) implicit by interpretation of formats for referenced cells. There is no strict data typing other than the distinction between text and number, and the text type is “arbitrarty length string”. In some contexts, formulas will also attempt to interpret text cells as number. This interpretation is fairly predictable but not intuitively obvious, and differs from the behavior of other spreadsheet applications.

A cell range behaves much like an array. You can name a range, effectively creating a named array. Data types of cells within such a range is not restricted like you’d expect for an array in programming languages.

Functions can return a third result type, namely an error signal.

There are functions for handling complex numbers. They require that real + imaginary portion be textually represented.

For StarBasic, the builtin macro language

See this reference. Boolean is separate from numeric, and there are several numeric types including fixed point (currency) and integer which have implications towards calculations. Structured data types also available.

Otherwise

Were you thinking of any particular application, one particular type of data you need to handle, or is your interest merely academical?