How to make LibreOffice Writer change keyboard language automatically to match surrounding text?

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No, but it would be a good feature. Consider filing an enhancement request. Automatic keyboard switching is possible to implement cross-platform, for example SIL FieldWorks.

To others who know more about Ask LO than I do -- this question was already asked. Should this be flagged as a duplicate?

Looks like the question has been answered over there: no. Given that LibreOffice is designed to be cross-platform, I wouldn't expect such a feature to exist.

You may also want to read this older thread on the question which was unnecessarily closed.

As there isn't such a feature, next question may be if it can be established based on user code.
There was a thread recently (concerning localized dates) to which I contributed the following piece of user code in BASIC:

Function getCurrentCharLocale(pDoc)
theCtrl = pDoc.CurrentController
theVC   = theCtrl.GetViewCursor
theLoc  = theVC.CharLocale
REM If the current selection is not unambiguous regarding the Locale then
REM TypeName(theLoc) = "Empty".
REM Otherwise a CharLocale has three attributes: .Language .Country .Variant
REM A collapsed ViewCursor ("Caret") should always return non-empty CharLocale except
REM it was actually set empty (no language).
getCurrentCharLocale = theLoc  
End Function

The .CharLocale property is a structure containing the properties .Language .Country and .Variant.
Based on this info you will need to call a script for changing the keyboard settings. How to do so will depend on the Operating System - if possible at all. It's not my field.