You didn’t mention the type of OLE object you inserted.
I experimented with a Calc spreadsheet. It initially comes as it is formatted.
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right-click on it and Edit
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select the cells you want to change
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apply the target style or create a new on
CAUTION! this will also change the formatting in the original document!
The spreadsheet is now styled differently from the original.
To summarize: edit your OLE object and apply a style.
EDIT 2020-02-09
In any LO component, when you Insert
>Object
>OLE Object
any “LO 7.0 xxx”, you create a new embedded document formatted according to the default template for this type of document. Therefore, the defaults you have set in Writer do not apply.
To have consistent styles between the Writer container and the embedded OLE object, either customise the default template for the other component or when editing the OLE object change the styles. The styles shown in the right style pane are those of the selected object. If you change them, this will be done only for the OLE object, which might be preferable if you don’t want to mess up the default template in case the defaults are different between OLE objects in Writer and autonomous spreadsheets, drawings or whatever.
However I question the insertion of a drawing as an OLE object. This may be justified for spreadsheets which are susceptible to be updated, but generally a drawing is frozen. You’ll have less trouble if you selecting the part of the drawing you need (so that you can have several drawing in a Draw page and keep the Draw document as a store) and paste it into the Writer document. It then lie in a frame which you can anchor in various ways and position it at will.
If you eventually modify the drawing, you just replace it in Writer.
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