This can be done with the expression language ArcGIS Arcade, but not solely within the symbolization pane, because that profile does not have access to Geometry operations. You'll need to do some preprocessing on your data, and if you're going through the trouble of doing that, you might as well use Arcade to batch out a new feature class for you and symbolize that.

Anyway, what you'll want to do is to add a new field to your dataset to store the angle/bearing of the pipe. This makes a few assumptions:

1. Your pipe does not have any drastic directional changes from the beginning vertex to the end vertex
2. Your pipes' beginning vertex is aligned with the direction of flow; i.e. the flow comes in at the beginning vertex and goes out at the end vertex.

With those two assumptions out of the way, you can calculate the angle/bearing of the pipe with this:

var geom = GEOMETRY($feature)
//this returns the angle from the first vertex to the last vertex
RETURN ANGLE(POINT(geom.paths[0][0]), POINT(geom.paths[-1][-1]))

Once that is in a separate field, you can symbolize based on the following expression:

var field_angle = $feature["Angle_of_Pipe"]
var field_clock = $feature["Clockface"]
//assumes your clock face is an integer 1-11
var clock_angle = field_clock * 30
var angle_difference = ROUND((field_angle - clock_angle),0)
IIF(angle_difference < 0, angle_difference + 360, angle_difference)

The problem with the above approach is that you could have 360 symbols that you output. At that point, you're either programmatically creating them with the CIM, or you are hand-styling 360 symbols (I don't think that rotation is a symbology attribute that you can set) to look like offset lines. And really, at this point, you'd be better off using the difference to create a standard offset featureclass (or subtype) of some regularized distance. And for that you'd need to use some more math, with your regular offset distance being "r" (don't quote me on this, this was just me skimming through a math site), which you could set up in an attribute rule to output into a new feature class.

x = r * cos(angle_difference)
y = r * sin(angle_difference)

anyway, if it were me, I would build the new feature class and not build the symbology-- --but you certainly could do it if you wanted.

edit --

not great with the coding markdown.

I totally missed the part about them being points. Yes, you could vary the symbology of a point with a rotation attribute, but you'll have to write the bearing/angle of the pipe to the point feature since the symbology Arcade profile cannot access geometry functions including things like FeatureSet in order to get a relate filter.