Hi,
you could try the plugin QNEAT3 which supports network based
origin-destination matrices between points of one layer or multiple sets
of points in two layers out of the box. The plugin is available through
the QGIS plugin repository and gets loaded in the processing toolbox,
the algorithms you are looking for are called 'OD Matrix from Points as
Table' or 'OD Matrix from Layers as Table'. The distance that is output
to the matrix is measured based on the provided network layer.
For more info on the plugin you can checkout https://root676.github.io/
I hope this helps!
Best, Clemens
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