It's clear to me that this line of discussion has a fundamental problem...

Understanding is the key to solution, and we still aren't connecting.

My understanding is that EXCEL has two modes of operation with functions:
(1) Worksheet (types include - database, date and time, engineering,
financial, information, logical, lookup and reference, math and trigonometry,
statistical, text, and external)
(2) VBA macro (more than I can list here, some of which resemble worksheet
functions with different spellings)

Sometimes we can invoke worksheet functions in VBA macro through a specific
invocation (e.g. Application.WorksheetFunction.Max). I'm trying not to resort
to macros, because the workbook will be used by folks who won't be able to
use them.

You brought up CELL as a worksheet Information Function - I didn't. The
documentation on CELL options didn't appear to address "interior color fill".
Macros can refer to the background cell color /pattern by invoking commands
like:

Workbooks("Book1").Worksheets("Sheet1").Range("Ran ge1").Interior.ColorIndex
or,
With Worksheets("Sheet1").Rectangles(1).Interior
.Pattern = xlChecker
.PatternColorIndex = 5
End With
or,
With Worksheets("Sheet1").Rectangles(1).Interior
.Pattern = xlGrid
.PatternColor = RGB(255,0,0)
End With
or,
Worksheets("Sheet1").Range("A1").Style.IncludePatt erns <boolean

so that the color's /pattern's code [unique identfier(s)] can be used as an
argument for IF...THEN filtering.

I'm looking for a non-macro, worksheet function that can address the
interior fill color /pattern. The colors that appear in my spreadsheet cells
of interest, are independent of the alphabetic /numeric contents values that
accompany them.

Apparently, there is no such defined MS Excel worksheet function that
extracts that information. That being the case, the response to my question
should be "No, there is no such simple solution without going macro." That
would have satisfied the query.